Find all School-related info fast with the new School-Specific MBA Forum

It is currently 29 May 2016, 07:51
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the diagram above, <PQR is a right angle, and QS is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 79
Followers: 1

Kudos [?]: 121 [0], given: 26

In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 05 May 2012, 19:37
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

65% (02:25) correct 35% (02:31) wrong based on 169 sessions

HideShow timer Statistics

Attachment:
Geometry.jpg
Geometry.jpg [ 3.7 KiB | Viewed 5666 times ]
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 May 2012, 02:25, edited 1 time in total.
Edited the question
1 KUDOS received
Intern
Intern
avatar
Joined: 06 May 2012
Posts: 2
Followers: 0

Kudos [?]: 1 [1] , given: 4

Re: Geometry [#permalink]

Show Tags

New post 06 May 2012, 02:16
1
This post received
KUDOS
is it true?

25^2 + qs^2 = qp^2
4^2 + qs^2 = qr^2
and then (by sum them) you have:
625+16+2(qs^2)=qp^2+qr^2 *
and you know from the main triangle:
pq^2+qr^2=(pr)^2=(25+4)^2=841 **

from * and ** we have:

pq^2 +qr^2 = 841 = 625+16+2qs^2
2qs^2=841-641= 200
qs=10
then the area of PQR is:
10* (25+4)/2 = 145
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33061
Followers: 5772

Kudos [?]: 70789 [3] , given: 9857

Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 06 May 2012, 02:43
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
BhaskarPaul wrote:
Attachment:
Geometry.jpg
Geometry.jpg [ 3.7 KiB | Viewed 5648 times ]
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined


Perpendicular to the hypotenuse always divides the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QS divides right triangle PRQ into two similar triangles PQS and QRS (which are also similar to the big triangle PRQ). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles).

So, PS/QS=QS/SR --> QS^2=PS*SR=25*4=100 --> QS=10 --> area of PQR equals to 1/2*PR*QS=1/2*(PS+SR)*QS=1/2*29*10=145.

Answer: B.

For more on check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 79
Followers: 1

Kudos [?]: 121 [0], given: 26

Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 06 May 2012, 15:58
Bunuel wrote:
BhaskarPaul wrote:
Attachment:
Geometry.jpg
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined


Perpendicular to the hypotenuse always divides the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QS divides right triangle PRQ into two similar triangles PQS and QRS (which are also similar to the big triangle PRQ). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles).

So, PS/QS=QS/SR --> QS^2=PS*SR=25*4=100 --> QS=10 --> area of PQR equals to 1/2*PR*QS=1/2*(PS+SR)*QS=1/2*29*10=145.

Answer: B.

For more on check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.



ya that helps , great
Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 79
Followers: 1

Kudos [?]: 121 [0], given: 26

Re: Geometry [#permalink]

Show Tags

New post 14 May 2012, 04:23
mehdi2012 wrote:
is it true?

25^2 + qs^2 = qp^2
4^2 + qs^2 = qr^2
and then (by sum them) you have:
625+16+2(qs^2)=qp^2+qr^2 *
and you know from the main triangle:
pq^2+qr^2=(pr)^2=(25+4)^2=841 **

from * and ** we have:

pq^2 +qr^2 = 841 = 625+16+2qs^2
2qs^2=841-641= 200
qs=10
then the area of PQR is:
10* (25+4)/2 = 145



This is also a good way to solve this problem if we find it difficult to apply similarity of triangles, though we have to find the squares of some numbers .
Intern
Intern
avatar
Joined: 19 Feb 2013
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: Geometry [#permalink]

Show Tags

New post 31 Jul 2013, 07:00
mehdi2012 wrote:
is it true?

25^2 + qs^2 = qp^2
4^2 + qs^2 = qr^2
and then (by sum them) you have:
625+16+2(qs^2)=qp^2+qr^2 *
and you know from the main triangle:
pq^2+qr^2=(pr)^2=(25+4)^2=841 **

from * and ** we have:

pq^2 +qr^2 = 841 = 625+16+2qs^2
2qs^2=841-641= 200
qs=10
then the area of PQR is:
10* (25+4)/2 = 145






How do we figure out which side is proportional to which using angles? :S
Intern
Intern
avatar
Joined: 02 Feb 2012
Posts: 29
GPA: 4
Followers: 0

Kudos [?]: 12 [0], given: 35

Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 01 Aug 2013, 20:37
Bunuel wrote:
BhaskarPaul wrote:
Attachment:
Geometry.jpg
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined


Perpendicular to the hypotenuse always divides the triangle into two triangles with the same properties as the original triangle.

Thus, the perpendicular QS divides right triangle PRQ into two similar triangles PQS and QRS (which are also similar to the big triangle PRQ). Now, in these three triangles the ratio of the corresponding sides will be equal (corresponding sides are the sides opposite the same angles).

So, PS/QS=QS/SR --> QS^2=PS*SR=25*4=100 --> QS=10 --> area of PQR equals to 1/2*PR*QS=1/2*(PS+SR)*QS=1/2*29*10=145.

Answer: B.

For more on check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.


Corresponding angles are QPS and QRS right.
In that case, it must be PS/QS=SR/QS..

Please let me know where I am wrong...
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9687
Followers: 466

Kudos [?]: 120 [0], given: 0

Premium Member
Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 28 Feb 2015, 13:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 14 Oct 2013
Posts: 48
GMAT 1: Q V
Followers: 0

Kudos [?]: 6 [0], given: 120

GMAT ToolKit User
Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 24 May 2015, 20:27
Why do we write the proportion inversely as PS/QS=QS/QR? I wrote it as QS/SR=QS/PS and then got stuck from there but wondering why we choose to write the proportion that way.
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6578
Location: Pune, India
Followers: 1794

Kudos [?]: 10793 [1] , given: 211

Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 24 May 2015, 21:54
1
This post received
KUDOS
Expert's post
healthjunkie wrote:
Why do we write the proportion inversely as PS/QS=QS/QR? I wrote it as QS/SR=QS/PS and then got stuck from there but wondering why we choose to write the proportion that way.


What made you think that QS/SR=QS/PS is the correct relation?
I assume you found that the two small triangles are similar to each other. The point is how are they similar to each other? They are similar because they are both similar to the big triangle PQR.
Angle PQR = Angle QSP = angle QSR = 90 degrees
Ange P is common to PQR and PSQ so by AA, triangle PQR is similar to triangle PSQ - note the naming of the triangles. The angles which are equal are placed in corresponding positions. Angle P is common so it is the first vertex of each triangle. Then angle Q = angle S so we have Q and S as second vertices and the leftover as third vertices to get PQR and PSQ.

Similarly, angle R is common to triangle PQR and triangle QSR so by AA, triangle PQR is similar to triangle QSR - the naming of the triangles should be in order to ensure that you get the corresponding sides correctly.

So triangle PQR is similar to triangles PSQ and QSR. Now you know the corresponding sides:

PS/QS (Sides made by first two underlined letters)= SQ/SR (sides made by next two letters) = PQ/QR (sides made by first and third letters)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 14 Oct 2013
Posts: 48
GMAT 1: Q V
Followers: 0

Kudos [?]: 6 [0], given: 120

GMAT ToolKit User
Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 25 May 2015, 09:35
Ah that makes sense, I was assuming the smaller triangles were similar to eachother as opposed them both being similar because they're similar to the larger triangle. Makes sense now!
Manager
Manager
avatar
Joined: 02 May 2014
Posts: 121
Schools: ESADE '16, HKU'16, SMU '16
GMAT 1: 620 Q46 V30
Followers: 0

Kudos [?]: 35 [0], given: 475

GMAT ToolKit User
Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 02 Jun 2015, 20:32
healthjunkie wrote:
Ah that makes sense, I was assuming the smaller triangles were similar to eachother as opposed them both being similar because they're similar to the larger triangle. Makes sense now!


Hi healthjunkie ,

All 3 triangles are similar. PQR ~ PSQ ~ QSR . U can try to prove it using AAA. Lemme know if u have any doubts on that.

Thanks!
1 KUDOS received
Manager
Manager
avatar
Joined: 24 Jun 2012
Posts: 103
GPA: 3.84
Followers: 3

Kudos [?]: 21 [1] , given: 69

Reviews Badge CAT Tests
Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 02 Jun 2015, 22:02
1
This post received
KUDOS
when we draw perpendicular then the sides of the two triangle are in same ratio
small side of large triangle/ large side of large triangle = small side of small triangle/large side of small triangle
we know PQS is large triangle and QSR is smaller triangle
PQS and QSR share the same height QS and angle QSR = QSP which confirms that the sides must be in same ratio
thus we know PS = 25 and RS = 4
we can write
25/QS = QS/4
100 = QS^2
10 = QS
now we know height = 10 and PR = 25+4 = 29
area of the triangle = 1/2(10)(29) = 145
Its B
_________________

Push yourself again and again. Don't give an inch until the final buzzer sounds. -Larry Bird
Success isn't something that just happens - success is learned, success is practiced and then it is shared. -Sparky Anderson
-S

SVP
SVP
avatar
Joined: 17 Jul 2014
Posts: 1614
Location: United States
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.56
WE: General Management (Transportation)
Followers: 10

Kudos [?]: 164 [0], given: 104

GMAT ToolKit User Premium Member Reviews Badge
Re: In the diagram above, <PQR is a right angle, and QS is [#permalink]

Show Tags

New post 11 Apr 2016, 19:09
Joy111 wrote:
Attachment:
Geometry.jpg
In the diagram above, <PQR is a right angle, and QS is perpendicular to PR. If PS has a length of 25 and SR has a length of 4, what is the area of triangle PQR?

A. 125
B. 145
C. 240
D. 290
E. It cannot be determined


right from the start I knew there's something with the similar triangles...
P is the same, and 90 degree angle is the same. it means that Q1 angle is equal to R angle.
and Q2 angle is equal to P angle.

now we have 2 right triangles..similar to each other.
leg 25 and height x for example
leg 4 and height x.

so:
25 corresponds to the x side of the smaller triangle, scale factor thus must be 25/x
x corresponds to the side equal to 4. so scale factor is x/4
of course the scale factor is the same...so we can set these two equal: 25/x = x/4 = cross multiply -> x^2 = 100, x=10.
base=29, height =10. 29x10/2 = 145.
Re: In the diagram above, <PQR is a right angle, and QS is   [#permalink] 11 Apr 2016, 19:09
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic In the diagram above, S is the center of the circle. If QS = 5 and QR Bunuel 9 02 Mar 2015, 08:33
18 Experts publish their posts in the topic In the diagram to the right, triangle PQR has a right angle sudeeptasahu29 12 29 Mar 2014, 00:17
6 Experts publish their posts in the topic In the diagram above, angle measures in degrees are marked mikemcgarry 4 04 Jun 2013, 11:27
60 Experts publish their posts in the topic In the diagram, triangle PQR has a right angle at Q and a enigma123 25 05 Feb 2012, 16:54
17 Experts publish their posts in the topic In the diagram to the right, triangle PQR has a right angle jimjohn 6 31 Oct 2007, 09:07
Display posts from previous: Sort by

In the diagram above, <PQR is a right angle, and QS is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.