Last visit was: 27 Apr 2026, 04:41 It is currently 27 Apr 2026, 04:41
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
505-555 (Easy)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 27 Apr 2026
Posts: 109,928
Own Kudos:
811,525
 [2]
Given Kudos: 105,914
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,928
Kudos: 811,525
 [2]
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 01:15
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

84% (02:17) correct 16% (02:51) wrong based on 73 sessions

History

Date
Time
Result
Not Attempted Yet

The length of the arc PQ in the quarter circle shown is \(10\pi\). If RS is 12, what is the area of the rectangle?

A. 172
B. 178
C. 186
D. 192
E. 198


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
2020-10-27_14-09-47.png
2020-10-27_14-09-47.png [ 34.9 KiB | Viewed 3005 times ]
ShowHide Answer
Official Answer
D
User avatar
rajatchopra1994
User avatar
Joined: 16 Feb 2015
Last visit: 22 Jun 2024
Posts: 1,052
Own Kudos:
1,308
 [1]
Given Kudos: 30
Location: United States
Posts: 1,052
Kudos: 1,308
 [1]
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 01:37
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Explanation:

Length of arc = 10π
Angle is 90
10π = 2*π*r*(90/360)
10π = π*r*(1/2)
r = 20 which is diagonal of rectangle.
One side of rectangle is 12
Other side will be = √(400-256 = 16

Area of rectangle = 16×12 = 192

IMO-D

Posted from my mobile device
avatar
DongminShin
avatar
Joined: 12 Nov 2020
Last visit: 27 Jun 2021
Posts: 8
Own Kudos:
8
Given Kudos: 26
Posts: 8
Kudos: 8
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 02:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
rajatchopra1994
Explanation:

Length of arc = 10π
Angle is 90
10π = 2*π*r*(90/360)
10π = π*r*(1/2)
r = 20 which is diagonal of rectangle.
One side of rectangle is 12
Other side will be = √(400-256 = 16

Area of rectangle = 16×12 = 192

IMO-D

Posted from my mobile device
Show more

How did you interpret the question as r is a diagonal of the rectangle? It seems to me that the vertex of the rectangle doesn't touch the circular line.
avatar
SHRUJAL
avatar
Current Student
Joined: 04 Mar 2020
Last visit: 18 Mar 2025
Posts: 66
Own Kudos:
12
 [1]
Given Kudos: 79
Location: India
Schools: Tepper '24 (D) Fuqua '24 (D) Kenan-Flagler '24 (A) Johnson '24 (WL) NUS (D)
GMAT 1: 640 Q46 V30
GMAT 2: 730 Q49 V41
GRE 1: Q167 V150
GPA: 3.97
Products:
My Reviews
Schools: Tepper '24 (D) Fuqua '24 (D) Kenan-Flagler '24 (A) Johnson '24 (WL) NUS (D)
GMAT 2: 730 Q49 V41
GRE 1: Q167 V150
Posts: 66
Kudos: 12
 [1]
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 06:24
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The length of the arc PQ in the quarter circle shown is \(10\pi\). If RS is 12, what is the area of the rectangle?

A. 172
B. 178
C. 186
D. 192
E. 198


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
2020-10-27_14-09-47.png
Show more

Since one of the sides of the rectangle is 12 ,
The Area should be divisible by 12 .
From the options ,
Only 192 is div by 12

IMO D
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,680
Own Kudos:
1,469
 [1]
Given Kudos: 607
Location: United States
Posts: 1,680
Kudos: 1,469
 [1]
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 07:48
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The length of the arc PQ in the quarter circle shown is \(10\pi\). If RS is 12, what is the area of the rectangle?

A. 172
B. 178
C. 186
D. 192
E. 198
Show more

arcPQ=diameter.pi/4=10.pi
diameter=40
radius=20=diagonal.rectangle
20^2=12^2+x^2
400-144=x^2
x=16; 16*12=192
(D)
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 17 Dec 2025
Posts: 5,902
Own Kudos:
5,456
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,902
Kudos: 5,456
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 08:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SHRUJAL
Bunuel

The length of the arc PQ in the quarter circle shown is \(10\pi\). If RS is 12, what is the area of the rectangle?

A. 172
B. 178
C. 186
D. 192
E. 198


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
2020-10-27_14-09-47.png

Since one of the sides of the rectangle is 12 ,
The Area should be divisible by 12 .
From the options ,
Only 192 is div by 12

IMO D
Show more
This is the best shortcut, no use of \(10\pi\) in solving the question , answer myst be (D) 192
User avatar
carouselambra
User avatar
Current Student
Joined: 14 Mar 2018
Last visit: 28 Apr 2023
Posts: 297
Own Kudos:
451
Given Kudos: 43
Posts: 297
Kudos: 451
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 08:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

The length of the arc PQ in the quarter circle shown is \(10\pi\). If RS is 12, what is the area of the rectangle?

A. 172
B. 178
C. 186
D. 192
E. 198


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

Show Spoiler
Attachment:
2020-10-27_14-09-47.png
Show more

I solved this question in a completely different way.
If you closely look at the options, you notice that only 1 option is divisible by 12.

It is clearly stated in the question that the area of a rectangle is a multiple of 12. Hence IMO D is the answer.
avatar
DongminShin
avatar
Joined: 12 Nov 2020
Last visit: 27 Jun 2021
Posts: 8
Own Kudos:
8
Given Kudos: 26
Posts: 8
Kudos: 8
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 09:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Two questions here for those who thinks the diagonal is the radius of the circle and for those who solved this problem by dividing the choices by 12.

1. Apparently, the vertex of rectangle is not touching the quarter circle's line. But how can you tell the diagonal of rectangle to be the radius of the circle?
2. There is no any condition stated in the question that the height of rectangle need to be integer. But how can you conclude that (D) is the answer, only because (D) 192 is divisible by 12?
avatar
SHRUJAL
avatar
Current Student
Joined: 04 Mar 2020
Last visit: 18 Mar 2025
Posts: 66
Own Kudos:
12
Given Kudos: 79
Location: India
Schools: Tepper '24 (D) Fuqua '24 (D) Kenan-Flagler '24 (A) Johnson '24 (WL) NUS (D)
GMAT 1: 640 Q46 V30
GMAT 2: 730 Q49 V41
GRE 1: Q167 V150
GPA: 3.97
Products:
My Reviews
Schools: Tepper '24 (D) Fuqua '24 (D) Kenan-Flagler '24 (A) Johnson '24 (WL) NUS (D)
GMAT 2: 730 Q49 V41
GRE 1: Q167 V150
Posts: 66
Kudos: 12
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 11:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DongminShin
Two questions here for those who thinks the diagonal is the radius of the circle and for those who solved this problem by dividing the choices by 12.

1. Apparently, the vertex of rectangle is not touching the quarter circle's line. But how can you tell the diagonal of rectangle to be the radius of the circle?
2. There is no any condition stated in the question that the height of rectangle need to be integer. But how can you conclude that (D) is the answer, only because (D) 192 is divisible by 12?
Show more
For the second point ,

Area = L*B
Area must be divisible by L and B

So , even if the width is not an integer
Suppose , Width = 10.5 , length = 12(as given)
Area = 10.5 * 12 = 126
If you divide ( Area / Length) , you will get the breadth . i.e (126/12) = 10.5
avatar
DongminShin
avatar
Joined: 12 Nov 2020
Last visit: 27 Jun 2021
Posts: 8
Own Kudos:
8
Given Kudos: 26
Posts: 8
Kudos: 8
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 16:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SHRUJAL
DongminShin
Two questions here for those who thinks the diagonal is the radius of the circle and for those who solved this problem by dividing the choices by 12.

1. Apparently, the vertex of rectangle is not touching the quarter circle's line. But how can you tell the diagonal of rectangle to be the radius of the circle?
2. There is no any condition stated in the question that the height of rectangle need to be integer. But how can you conclude that (D) is the answer, only because (D) 192 is divisible by 12?
For the second point ,

Area = L*B
Area must be divisible by L and B

So , even if the width is not an integer
Suppose , Width = 10.5 , length = 12(as given)
Area = 10.5 * 12 = 126
If you divide ( Area / Length) , you will get the breadth . i.e (126/12) = 10.5
Show more

Of course, the area of rectangle will be made by its width and length. But it doesn't mean it should be integers or decimal. This is my point.
For example, if the length of rectangle above is 43/3, the rectangle's area can be 172, by multiplaying its width(12) and length (43/3).

What I want to say again is there is nothing mentioned in the question that the length of rectangle should be ONLY integer and thus we should not neglect the possibility that the length can be a decimal.

Like what you have said "10.5 could be the length of rectangle", then other decimals(including both the terminating decimal and infinite decimal) such as 14.3333~(which can be expressed as 43/3) should be regarded as a possible answer too.

Posted from my mobile device
avatar
SHRUJAL
avatar
Current Student
Joined: 04 Mar 2020
Last visit: 18 Mar 2025
Posts: 66
Own Kudos:
12
Given Kudos: 79
Location: India
Schools: Tepper '24 (D) Fuqua '24 (D) Kenan-Flagler '24 (A) Johnson '24 (WL) NUS (D)
GMAT 1: 640 Q46 V30
GMAT 2: 730 Q49 V41
GRE 1: Q167 V150
GPA: 3.97
Products:
My Reviews
Schools: Tepper '24 (D) Fuqua '24 (D) Kenan-Flagler '24 (A) Johnson '24 (WL) NUS (D)
GMAT 2: 730 Q49 V41
GRE 1: Q167 V150
Posts: 66
Kudos: 12
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 19 Nov 2020, 22:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DongminShin
SHRUJAL
DongminShin
Two questions here for those who thinks the diagonal is the radius of the circle and for those who solved this problem by dividing the choices by 12.

1. Apparently, the vertex of rectangle is not touching the quarter circle's line. But how can you tell the diagonal of rectangle to be the radius of the circle?
2. There is no any condition stated in the question that the height of rectangle need to be integer. But how can you conclude that (D) is the answer, only because (D) 192 is divisible by 12?
For the second point ,

Area = L*B
Area must be divisible by L and B

So , even if the width is not an integer
Suppose , Width = 10.5 , length = 12(as given)
Area = 10.5 * 12 = 126
If you divide ( Area / Length) , you will get the breadth . i.e (126/12) = 10.5

Of course, the area of rectangle will be made by its width and length. But it doesn't mean it should be integers or decimal. This is my point.
For example, if the length of rectangle above is 43/3, the rectangle's area can be 172, by multiplaying its width(12) and length (43/3).

What I want to say again is there is nothing mentioned in the question that the length of rectangle should be ONLY integer and thus we should not neglect the possibility that the length can be a decimal.

Like what you have said "10.5 could be the length of rectangle", then other decimals(including both the terminating decimal and infinite decimal) such as 14.3333~(which can be expressed as 43/3) should be regarded as a possible answer too.

Posted from my mobile device
Show more
The question is asking about the area . Not the length of the other side .
So it doesn't matter whether the length of the rectangle is 43/3 or \sqrt{111} or any other decimal (terminating and nonterminating)
This doesnt change the fact that area will still be divisible by 12 !!
avatar
DongminShin
avatar
Joined: 12 Nov 2020
Last visit: 27 Jun 2021
Posts: 8
Own Kudos:
8
Given Kudos: 26
Posts: 8
Kudos: 8
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 20 Nov 2020, 00:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SHRUJAL
DongminShin
Two questions here for those who thinks the diagonal is the radius of the circle and for those who solved this problem by dividing the choices by 12.

1. Apparently, the vertex of rectangle is not touching the quarter circle's line. But how can you tell the diagonal of rectangle to be the radius of the circle?
2. There is no any condition stated in the question that the height of rectangle need to be integer. But how can you conclude that (D) is the answer, only because (D) 192 is divisible by 12?
For the second point ,

Area = L*B
Area must be divisible by L and B

So , even if the width is not an integer
Suppose , Width = 10.5 , length = 12(as given)
Area = 10.5 * 12 = 126
If you divide ( Area / Length) , you will get the breadth . i.e (126/12) = 10.5
Show more

Please remind that I don't have any intention to make you feel bad,
but I need to tell you or other people who thought (D) is the final answer only because 192 is divisible by 12 that YOU'RE APPROACH IS WRONG.

Let me first repeat that the length of rectangle can be any kinds of real number. It could be an integer or an integer.
Based on your approach, 192 is the final answer, because 192 is 12 * 16, where 16 is an integer.
But according to your approach,
why not the length be 172/12? so that it could make the area to be 172?
why not the length be 178/12? so that it could make the area to be 178?
why not the length be 186/12? so that it could make the area to be 186?
why not the length be 198/12? so that it could make the area to be 198?

It seems that you didn't get my point at all.
Area is a product of the length(l) and the width(12).
But there is no any condition stated that length should be an integer.
That will mean that the length does not necessarily need to be an integer. It could be any real number.

Assuming that the diagonal of rectangle is not touching the quarter circle's line.
If you apply the Pythagorean theorem by yourself, you are gonna know that the length of rectangle should be less 16 since the diagonal is shorter than radius.
And at that point, you would be able to narrow your answer options from (A) to (C), NOT (D) and (E).

---------------------------------

The reason of choosing (D) as an answer should be only because you assumed that the diagonal is touching the quarter circle's line. At the same time assuming the picture is drawn incorrectly.
But the reason of choosing (D) as an answer should NOT be because you thought the length should be an integer which makes the 192 divisible by 12.
User avatar
Nups1324
User avatar
Joined: 05 Jan 2020
Last visit: 12 Sep 2023
Posts: 104
Own Kudos:
65
Given Kudos: 353
Posts: 104
Kudos: 65
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 20 Nov 2020, 02:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DongminShin
SHRUJAL
DongminShin
Two questions here for those who thinks the diagonal is the radius of the circle and for those who solved this problem by dividing the choices by 12.

1. Apparently, the vertex of rectangle is not touching the quarter circle's line. But how can you tell the diagonal of rectangle to be the radius of the circle?
2. There is no any condition stated in the question that the height of rectangle need to be integer. But how can you conclude that (D) is the answer, only because (D) 192 is divisible by 12?
For the second point ,

Area = L*B
Area must be divisible by L and B

So , even if the width is not an integer
Suppose , Width = 10.5 , length = 12(as given)
Area = 10.5 * 12 = 126
If you divide ( Area / Length) , you will get the breadth . i.e (126/12) = 10.5

Please remind that I don't have any intention to make you feel bad,
but I need to tell you or other people who thought (D) is the final answer only because 192 is divisible by 12 that YOU'RE APPROACH IS WRONG.

Let me first repeat that the length of rectangle can be any kinds of real number. It could be an integer or an integer.
Based on your approach, 192 is the final answer, because 192 is 12 * 16, where 16 is an integer.
But according to your approach,
why not the length be 172/12? so that it could make the area to be 172?
why not the length be 178/12? so that it could make the area to be 178?
why not the length be 186/12? so that it could make the area to be 186?
why not the length be 198/12? so that it could make the area to be 198?

It seems that you didn't get my point at all.
Area is a product of the length(l) and the width(12).
But there is no any condition stated that length should be an integer.
That will mean that the length does not necessarily need to be an integer. It could be any real number.

Assuming that the diagonal of rectangle is not touching the quarter circle's line.
If you apply the Pythagorean theorem by yourself, you are gonna know that the length of rectangle should be less 16 since the diagonal is shorter than radius.
And at that point, you would be able to narrow your answer options from (A) to (C), NOT (D) and (E).

---------------------------------

The reason of choosing (D) as an answer should be only because you assumed that the diagonal is touching the quarter circle's line. At the same time assuming the picture is drawn incorrectly.
But the reason of choosing (D) as an answer should NOT be because you thought the length should be an integer which makes the 192 divisible by 12.
Show more

Dear experts,

There is a confusion regarding the correct approach to solve this problem. Please help us out with the correct solution.

Bunuel chetan2u GMATinsight IanStewart ScottTargetTestPrep yashikaaggarwal VeritasKarishma BrentGMATPrepNow egmat EMPOWERgmatRichC

DongminShin SHRUJAL

Thank you :)

Posted from my mobile device
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 24 Apr 2026
Posts: 4,143
Own Kudos:
11,281
Given Kudos: 99
Expert
Expert reply
Posts: 4,143
Kudos: 11,281
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 20 Nov 2020, 03:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DongminShin is correct - you can't use divisibility here, because there's no reason the width of the rectangle needs to be an integer, and thus no reason the area needs to be divisible by 12.

The question isn't answerable unless the rectangle touches the circumference of the circle. It's true there appears to be a gap between the top right corner of the rectangle and the circle, but that must be an error in the diagram. If you assume the top right corner of the rectangle is a point on the circle, then rajatchopra1994 and others have posted perfect solutions above.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 27 Apr 2026
Posts: 11,229
Own Kudos:
45,026
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,026
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 20 Nov 2020, 04:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nups1324

Dear experts,

There is a confusion regarding the correct approach to solve this problem. Please help us out with the correct solution.
Show more

There is no reason to believe the width to be an integer. It could easily be a fraction or even some root.
The correct way is to find the width by using diagonal(should be equal to the radius to make sense) and RS. The diagram has not been made properly and you will not find such error in actuals. So, solve the question taking the vertex on the circumference.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 27 Apr 2026
Posts: 22,286
Own Kudos:
26,539
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,286
Kudos: 26,539
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 22 Nov 2020, 21:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Nups1324

Dear experts,

There is a confusion regarding the correct approach to solve this problem. Please help us out with the correct solution.

Bunuel chetan2u GMATinsight IanStewart ScottTargetTestPrep yashikaaggarwal VeritasKarishma BrentGMATPrepNow egmat EMPOWERgmatRichC

DongminShin SHRUJAL

Thank you :)

Posted from my mobile device
Show more

First of all, the divisibility argument is not applicable for this question because it is not mentioned anywhere that the sides of the rectangle are integers. It is only a fortunate coincidence that the only answer choice that produces an integer when divided by 12 turns out to be the correct answer. If I were the author of this question, I would make the correct answer some value which is not divisible by 12 and also make sure that there is one answer choice that is divisible by 12. One should always keep in mind that divisibility is a notion which makes sense for integers only. If we allow non-integer quotients, everything is divisible by everything and the term "divisibility" loses its meaning. If the question told us that the sides of the rectangle were integers, it would be 100% correct to eliminate some of the answer choices using the divisibility argument. However, that is not the case for this question.

Next, the only way this question has a unique answer is if the rectangle is touching the arc PQ. If a vertex of the rectangle is not on the arc PQ, then the side of the rectangle contained within PS could have any length less than 16. Recall that diagrams are not drawn to scale unless noted otherwise. This means that if there was a gap between the vertex of the rectangle and the arc PQ, we would not be able to judge the size of this gap by looking at the figure. This implies that the other side of the rectangle could have length 15 or 15.5 or 15.9 so that the gap is really tiny, or the same length could be 1 or 2 so that the gap is huge. In that case, it would be possible for the area of the rectangle to be any value less than 192. The question should have labeled all vertices of the rectangle and told us that the vertex which looks like it is on the arc PQ is indeed on the arc PQ.
User avatar
Harsh9676
User avatar
Joined: 18 Sep 2018
Last visit: 27 Feb 2023
Posts: 239
Own Kudos:
228
Given Kudos: 322
Location: India
Concentration: Finance, International Business
GMAT 1: 690 Q49 V36
GPA: 3.72
WE:Investment Banking (Finance: Investment Banking)
Products:
My Reviews
GMAT 1: 690 Q49 V36
Posts: 239
Kudos: 228
The length of the arc PQ in the quarter circle shown is 10pi. If RS is 22 Nov 2020, 23:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ans D

Now the Radius of the Quarter circle >> (90/360) = 10pi / 2 Pi r

Therefore R = 20

Also given length of the rectangle = 12 and the radius of the quarter circle would be equal to the length of the diagonal

Length of diagonal = Sqrt (L^2 + W^2)

===> 20 = sqer (144 + w^2)
===> w = 16

Now, Area of rectangle = L * W >> 16 * 12 = 196
Moderators:
Bunuel
Math Expert
109928 posts
Krunaal
Tuck School Moderator
852 posts