Last visit was: 07 Jun 2026, 01:49 It is currently 07 Jun 2026, 01:49
Home
Messages
MBA Fair
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
805+ (Hard)|   Geometry|      
User avatar
Princ
User avatar
Joined: 22 Feb 2018
Last visit: 04 May 2025
Posts: 350
Own Kudos:
932
 [9]
Given Kudos: 34
Posts: 350
Kudos: 932
 [9]
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS 06 Jul 2018, 06:25
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

41% (03:03) correct 59% (03:22) wrong based on 44 sessions

History

Date
Time
Result
Not Attempted Yet
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS is inscribed in the triangle as shown in the figure. Find the side of the square?
Attachment:
Capture.PNG
Capture.PNG [ 4.97 KiB | Viewed 13061 times ]

A) \(3\)
B) \(\frac{120}{37}\)
C) \(4\)
D) \(\frac{40}{9}\)
E) \(\frac{120}{23}\)
ShowHide Answer
Official Answer
B
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 24 May 2026
Posts: 1,923
Own Kudos:
6,907
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,923
Kudos: 6,907
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS 06 Jul 2018, 07:02
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This question can be solved by using similarity of triangles, see the sketch attached.
Attachments

WhatsApp Image 2018-07-06 at 19.30.14.jpeg
WhatsApp Image 2018-07-06 at 19.30.14.jpeg [ 67.04 KiB | Viewed 13038 times ]

User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 06 Jun 2026
Posts: 11,241
Own Kudos:
45,348
Given Kudos: 338
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: 11,241
Kudos: 45,348
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS 07 Jul 2018, 01:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Princ
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS is inscribed in the triangle as shown in the figure. Find the side of the square?
Attachment:
The attachment Capture.PNG is no longer available

A) \(3\)
B) \(\frac{120}{37}\)
C) \(4\)
D) \(\frac{40}{9}\)
E) \(\frac{120}{23}\)
Show more

If we look at sides as of \(\triangle{ABC}\), 6, 8, 10, it tells us that it is 3:4:5 triangle..

Now let side of square be x and PQ is || to AC (opposite sides of square)
in \(\triangle{BPQ}\), the sides too will be in 3:4:5 = BQ : BP : x
so BP = \(\frac{4x}{5}\)

now \(\triangle{CPS}\) and \(\triangle{ABC}\) are also similar and hence 3:4:5 \(\triangle\)
now 3:4:5=PS:CS:CP=x:CS:CP
so 3 = x, so 5 = CP = \(\frac{5x}{3}\)

Now BP+CP=AB...........\(\frac{4x}{5}+\frac{5x}{3}=8.................\frac{12x+25x}{15}=8..............\frac{37x}{15}=8\).
\(x=\frac{8*15}{37}=\frac{120}{37}\)

B
Attachments

Capture.PNG
Capture.PNG [ 13.79 KiB | Viewed 12440 times ]

User avatar
Princ
User avatar
Joined: 22 Feb 2018
Last visit: 04 May 2025
Posts: 350
Own Kudos:
932
 [1]
Given Kudos: 34
Posts: 350
Kudos: 932
 [1]
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS 07 Jul 2018, 02:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
OA: B
Given AB=6 ,BC = 8 , AC =10
Attachment:
Capture Ans.PNG
Capture Ans.PNG [ 14.06 KiB | Viewed 12126 times ]
As can be seen from figure above, all four \(\triangle\) i.e. \(\triangle\)ABC ,\(\triangle\)ARQ ,\(\triangle\)QBP ,\(\triangle\) PSC are similar.
Because of AA similarity as their corresponding angles are equal in measure.

Considering \(\triangle\) ABC and \(\triangle\) QBP ,we get
\(\frac{BP}{BC}=\frac{BQ}{AB}=\frac{PQ}{AC} = k\) (a constant)

We get \(QP=10k\) and \(BQ=6k\)

As all sides of a square are equal,QR will be also equal to QP i.e \(QR =10k\).

Considering \(\triangle\) ABC and \(\triangle\) QBP ,we get
\(\frac{QR}{BC}=\frac{AR}{AB}=\frac{AQ}{AC} = p\) (a constant)
\(\frac{QR}{BC}=\frac{AQ}{AC}\)
\(\frac{{10k}}{8}=\frac{AQ}{10}\)
\(AQ =\frac{{100k}}{8}=\frac{{25k}}{2}\)

\(AB =BQ+AQ\)
\(6= 6k + \frac{{25k}}{2}\)
\(k = \frac{12}{37}\)

Side of Square\(= 10k = 10* \frac{12}{37} =\frac{120}{37}\)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,178
Own Kudos:
1,128
Posts: 39,178
Kudos: 1,128
In right angle triangle ABC, AB = 6, BC = 8 and AC = 10. A square PQRS 19 Jan 2020, 16:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
111124 posts