Last visit was: 11 Jul 2025, 17:35 It is currently 11 Jul 2025, 17:35
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.
Close
Request Expert Reply
Confirm Cancel
avatar
aljatar
Joined: 08 Dec 2009
Last visit: 06 Jan 2012
Posts: 27
Own Kudos:
355
 [267]
Posts: 27
Kudos: 355
 [267]
12
Kudos
Add Kudos
254
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,635
Own Kudos:
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,635
Kudos: 740,500
 [161]
91
Kudos
Add Kudos
70
Bookmarks
Bookmark this Post
avatar
sleekmover
Joined: 23 Oct 2010
Last visit: 06 Feb 2015
Posts: 12
Own Kudos:
101
 [60]
Given Kudos: 6
Location: India
GMAT 2: 730  Q49  V41
Posts: 12
Kudos: 101
 [60]
46
Kudos
Add Kudos
14
Bookmarks
Bookmark this Post
General Discussion
avatar
Princas1
Joined: 02 Oct 2014
Last visit: 22 Feb 2018
Posts: 3
Own Kudos:
16
 [12]
Given Kudos: 1
Posts: 3
Kudos: 16
 [12]
7
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
It is a really good exercise.

Solving this one in a standard way brings a lot of confusion.
In my opinion it is a helpful here to know, that a square has a biggest area if the sum of length of bases is the same.
For example: If sum of bases is 8, the biggest possible area is 16, which is a square. (Other options 5x3=15; 6x2=12; 8x1=8)

Knowing this, we could easily eliminate answer choices that are other 200 because we know that diagonal is 200 and therefore the maximum area is 200^2/2 :)
Moreover, knowing the rule of square diagonal we could remove 200, because square diagonal would be base * sqrt(2) (90-45-45 formula)

And also 196 is a (14*14) so this means that diagonal is not integer and we could remove it also.

Hence, one answer choice is left:)

A :D
avatar
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,538
Own Kudos:
7,888
 [11]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,538
Kudos: 7,888
 [11]
8
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Say length of the park = x, width = (280-x)

\(200^2 = x^2 + (280-x)^2\)

\(2x^2 - 560x + (280^2 - 200^2) = 0\)

\(2x^2 - 560x + (280 + 200)(280 - 200) = 0\)

\(2x^2 - 560x + 480 * 80 = 0\)

\(x^2 - 280x + 480*40 = 0\)

Dimensions = 160 & 120

Area = 19200

Answer = A
avatar
mbaboop
Joined: 02 Sep 2015
Last visit: 19 Aug 2017
Posts: 22
Own Kudos:
24
 [18]
Given Kudos: 2
Location: United States
WE:Management Consulting (Consulting)
Products:
Posts: 22
Kudos: 24
 [18]
10
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.


diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle

using the ratio 3:4:5 for sides, and knowing c = 200, you can deduce the following

a=120
b=160

160x120=19,200

A is the answer.
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,488
 [15]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,488
 [15]
12
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Hi All,

It's important to remember that nothing about a GMAT question is ever 'random' - the wording and numbers/data are always carefully chosen. Thus, you can sometimes use the 'design' of a prompt to your advantage and spot the built-in patterns that are often there.

Here, notice how ALL of the numbers are relatively 'nice', round numbers - even the diagonal is a nice number (and that doesn't happen very often when dealing with rectangles).... Since the answer choices are also round numbers, it's likely that the triangles that are 'hidden' in this rectangle are based on one of the common right-triangle patterns (in this case, the 3/4/5 - since 200 is a multiple of 5).

Using that knowledge to our advantage, IF we had a 3/4/5 and the diagonal was 200, then that would be '40 times' 5... so the other two sides would be 40 times 4 and 40 times 3: 160 and 120. With those two side lengths, we'd have a perimeter of 2(160) + 2(120) = 560... and that is an exact MATCH for what we were told, so this MUST be the situation that we're dealing with.

At this point, the area can be calculated easily enough: (L)(W) = (160)(120) = 19,200

Final Answer:

GMAT assassins aren't born, they're made,
Rich
User avatar
LakerFan24
Joined: 26 Dec 2015
Last visit: 03 Apr 2018
Posts: 167
Own Kudos:
Given Kudos: 1
Location: United States (CA)
Concentration: Finance, Strategy
WE:Investment Banking (Finance: Venture Capital)
Posts: 167
Kudos: 677
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
Hi All,

It's important to remember that nothing about a GMAT question is ever 'random' - the wording and numbers/data are always carefully chosen. Thus, you can sometimes use the 'design' of a prompt to your advantage and spot the built-in patterns that are often there.

Here, notice how ALL of the numbers are relatively 'nice', round numbers - even the diagonal is a nice number (and that doesn't happen very often when dealing with rectangles).... Since the answer choices are also round numbers, it's likely that the triangles that are 'hidden' in this rectangle are based on one of the common right-triangle patterns (in this case, the 3/4/5 - since 200 is a multiple of 5).

Using that knowledge to our advantage, IF we had a 3/4/5 and the diagonal was 200, then that would be '40 times' 5... so the other two sides would be 40 times 4 and 40 times 3: 160 and 120. With those two side lengths, we'd have a perimeter of 2(160) + 2(120) = 560... and that is an exact MATCH for what we were told, so this MUST be the situation that we're dealing with.

At this point, the area can be calculated easily enough: (L)(W) = (160)(120) = 19,200

Final Answer:

GMAT assassins aren't born, they're made,
Rich

while you got the answer correct here, i wonder why you assume that just because 200 is a multiple of 5, that there is a hidden 3-4-5 triangle? does this need be true? is this based on a property/rule that I'm overlooking?
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,488
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,488
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi LakerFan24,

GMAT questions are almost always built around a pattern (and sometimes more than one pattern), so part of approaching questions efficiently is to think about the inherent patterns that could be involved. In addition, the 'world of math' is full of patterns that you can take advantage of (Number Properties, formulas, etc.).

Here, we're dealing with a rectangular park, so if you 'cut' the park from corner to opposite-corner, you'll end up with two right triangles. As a thought experiment, I want you to choose two random numbers for the two legs of the right triangle. Using the Pythagorean Theorem (A^2 + B^2 = C^2), you can calculate the diagonal. Now, how often do you actually end up with an INTEGER for that diagonal. Choose a few pairs of random numbers for the legs and you'll see that usually the diagonal is NOT an INTEGER... but here, the diagonal IS an integer (its length is 200). The answer choices to this question are all integers, meaning that the two sides of the rectangle are almost certainly integers. So, we're dealing with triangles that have integers for ALL 3 SIDES. By extension, that means the two triangles are likely one of the common 'magic' Pythagorean Triplets (the 3/4/5, 5/12/13 or a multiple of one them - since those triplets have a diagonal side that's an integer).

GMAT assassins aren't born, they're made,
Rich
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,059
 [13]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,059
 [13]
11
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
aljatar
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800

Let L and W equal the length and width of the rectangle respectively.

perimeter = 560
So, L + L + W + W = 560
Simplify: 2L + 2W = 560
Divide both sides by 2 to get: L + W = 280

diagonal = 200
The diagonal divides the rectangle into two RIGHT TRIANGLES.
Since we have right triangles, we can apply the Pythagorean Theorem.
We get L² + W² = 200²

NOTE: Our goal is to find the value of LW [since this equals the AREA of the rectangle]

If we take L + W = 280 and square both sides we get (L + W)² = 280²
If we expand this, we get: L² + 2LW + W² = 280²
Notice that we have L² + W² "hiding" in this expression.
That is, we get: + 2LW + = 280²

We already know that L² + W² = 200², so, we'll take + 2LW + = 280² and replace L² + W² with 200² to get:
2LW + 200² = 280²
So, 2LW = 280² - 200²
Evaluate: 2LW = 38,400
Solve: LW = 19,200

Answer: A

Cheers,
Brent
User avatar
MsInvBanker
Joined: 23 May 2018
Last visit: 16 Jun 2021
Posts: 658
Own Kudos:
224
 [4]
Given Kudos: 45
Location: Pakistan
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Assuming that the 560 feet perimeter of the park was a square, we get that one side would be 140 feet. For any parallelogram (of equal perimeter), square has the greatest area.

With 140feet for one side, we get the area 19600 sq ft.

The park, however, is a rectangle and will thus have an area less than a square.

We have only one option for this.

A. 19200
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Jul 2025
Posts: 21,091
Own Kudos:
26,140
 [6]
Given Kudos: 296
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: 21,091
Kudos: 26,140
 [6]
4
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
A rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

(A) 19200
(B) 19600
(C) 20000
(D) 20400
(E) 20800

We can let L = the length of the park and W = the width of the park. Our goal is to find the area of the park, i.e., the value of LW.

We can create the equations:

Perimeter = 560

2L + 2W = 560

L + W = 280

and

L^2 + W^2 = 200^2

Squaring the first equation, we have:

(L + W)^2 = 280^2

L^2 + W^2 + 2LW = 280^2

Substituting, we have:

200^2 + 2LW = 280^2

2LW = 280^2 - 200^2

2LW = (280 - 200)(280 + 200)

2LW = 80 x 480

LW = 40 x 480 = 19,200

Answer: A
User avatar
Shbm
Joined: 20 Jun 2018
Last visit: 02 Dec 2020
Posts: 65
Own Kudos:
Given Kudos: 86
Location: India
Posts: 65
Kudos: 16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ScottTargetTestPrep
Bunuel
A rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

(A) 19200
(B) 19600
(C) 20000
(D) 20400
(E) 20800

We can let L = the length of the park and W = the width of the park. Our goal is to find the area of the park, i.e., the value of LW.

We can create the equations:

Perimeter = 560

2L + 2W = 560

L + W = 280

and

L^2 + W^2 = 200^2

Squaring the first equation, we have:

(L + W)^2 = 280^2

L^2 + W^2 + 2LW = 280^2

Substituting, we have:

200^2 + 2LW = 280^2

2LW = 280^2 - 200^2

2LW = (280 - 200)(280 + 200)

2LW = 80 x 480

LW = 40 x 480 = 19,200

Answer: A




Shouldn't L square plus W square be equal to 200 rather than being equal to 200 square? Please assist.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Jul 2025
Posts: 21,091
Own Kudos:
26,140
 [1]
Given Kudos: 296
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: 21,091
Kudos: 26,140
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Shbm
ScottTargetTestPrep
Bunuel
A rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

(A) 19200
(B) 19600
(C) 20000
(D) 20400
(E) 20800

We can let L = the length of the park and W = the width of the park. Our goal is to find the area of the park, i.e., the value of LW.

We can create the equations:

Perimeter = 560

2L + 2W = 560

L + W = 280

and

L^2 + W^2 = 200^2

Squaring the first equation, we have:

(L + W)^2 = 280^2

L^2 + W^2 + 2LW = 280^2

Substituting, we have:

200^2 + 2LW = 280^2

2LW = 280^2 - 200^2

2LW = (280 - 200)(280 + 200)

2LW = 80 x 480

LW = 40 x 480 = 19,200

Answer: A




Shouldn't L square plus W square be equal to 200 rather than being equal to 200 square? Please assist.


200^2 is correct since it’s based on the Pythagorean theorem: a^2 + b^2 = c^2. Here, L^2 + W^2 = D^2 where D is the diagonal. Notice that on a rectangle, the short and long side together with the diagonal form a right triangle; that’s why the Pythagorean theorem is applicable.
User avatar
GMATGuruNY
Joined: 04 Aug 2010
Last visit: 08 Jul 2025
Posts: 1,345
Own Kudos:
3,661
 [1]
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,345
Kudos: 3,661
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aljatar
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800

ALWAYS LOOK FOR SPECIAL TRIANGLES.
Draw the rectangle and its diagonal:
Attachment:
diagonal_of_200.png
diagonal_of_200.png [ 4.63 KiB | Viewed 23861 times ]

Since diagonal AD is a multiple of 5 -- and every value in the problem is an INTEGER -- check whether triangle ABD is a multiple of a 3:4:5 triangle.
If each side of a 3:4:5 triangle is multiplied by 40, we get:
(40*3):(40*4):(40*5) = 120:160:200
The following figure is implied:
Attachment:
diagonal_of_200_1 (1).png
diagonal_of_200_1 (1).png [ 5.86 KiB | Viewed 23849 times ]

Check whether the resulting perimeter for rectangle ABCD is 560:
120+160+120+160 = 560
Success!
Implication:
For the perimeter of rectangle ABCD to be 560, triangle ABD must be a multiple of a 3:4:5 triangle with sides 120, 160 and 200.

Thus:
Area of rectangle ABCD = L * W = 160 * 120 = 19200

User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 06 Jul 2025
Posts: 1,294
Own Kudos:
1,889
 [12]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
GMAT 3: 770 Q50 V45
Posts: 1,294
Kudos: 1,889
 [12]
11
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning (starts at 0:15:06):
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
avatar
AbhaGanu
Joined: 09 Jun 2018
Last visit: 21 Aug 2021
Posts: 53
Own Kudos:
Given Kudos: 87
Posts: 53
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel why have you squared the diagonal?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,635
Own Kudos:
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,635
Kudos: 740,500
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AbhaGanu
Bunuel why have you squared the diagonal?

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.



So, in order to express D in terms of l and we w can write \(D^2 = l^2 + w^2\).

Hope it's clear.

Attachment:
1.png
1.png [ 2.38 KiB | Viewed 18574 times ]
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Isnt area of rectangle = 0.5*D1*D2 where D1 and D2 are diagonal of rectangle?? Please Confirm??
User avatar
GMATGuruNY
Joined: 04 Aug 2010
Last visit: 08 Jul 2025
Posts: 1,345
Own Kudos:
Given Kudos: 9
Schools:Dartmouth College
Expert
Expert reply
Posts: 1,345
Kudos: 3,661
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vedikadadhich
Isnt area of rectangle = 0.5*D1*D2 where D1 and D2 are diagonal of rectangle?? Please Confirm??

The formula above is valid for a KITE (a quadrilateral in which two pairs of ADJACENT sides are equal):
Attachment:
area of a kite.png
area of a kite.png [ 152.82 KiB | Viewed 20113 times ]
Note that a rhombus (with four equal sides) is a type of kite, as is a square (with four equal sides and four equal angles).
Thus, the formula can be used to find the area of a rhombus or square.
In the posted problem, no adjacent sides are equal, so the formula is not applicable.
 1   2   
Moderators:
Math Expert
102635 posts
PS Forum Moderator
688 posts