Last visit was: 26 Apr 2026, 17:18 It is currently 26 Apr 2026, 17:18
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
805+ (Hard)|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 26 Apr 2026
Posts: 109,910
Own Kudos:
811,440
 [7]
Given Kudos: 105,897
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: 109,910
Kudos: 811,440
 [7]
Through a point on the hypotenuse of a right triangle, lines are drawn 18 Mar 2019, 01:52
1
Kudos
Add Kudos
6
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:

95% (hard)

Question Stats:

32% (03:12) correct 68% (02:54) wrong based on 65 sessions

History

Date
Time
Result
Not Attempted Yet
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is


(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)
ShowHide Answer
Official Answer
D
User avatar
Sanjeetgujrall
User avatar
Joined: 04 Sep 2016
Last visit: 26 Apr 2024
Posts: 50
Own Kudos:
62
Given Kudos: 66
Location: Germany
GPA: 3
Posts: 50
Kudos: 62
Through a point on the hypotenuse of a right triangle, lines are drawn 09 Apr 2019, 03:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can someone explain why its D?

For it to construct a square doesnt the point on the hypotenuse have to be the mid point of it ?

Posted from my mobile device
avatar
ajmekal
avatar
Joined: 22 Mar 2019
Last visit: 03 Sep 2019
Posts: 3
Own Kudos:
2
Given Kudos: 69
Posts: 3
Kudos: 2
Through a point on the hypotenuse of a right triangle, lines are drawn 09 Apr 2019, 06:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sanjeetgujrall
Can someone explain why its D?

For it to construct a square doesnt the point on the hypotenuse have to be the mid point of it ?

Posted from my mobile device
Show more


This condition may or may not be true.
User avatar
Manas1212
User avatar
Joined: 31 Jul 2017
Last visit: 10 Aug 2019
Posts: 68
Own Kudos:
116
 [2]
Given Kudos: 474
Location: India
Schools: LBS '21 Anderson '21
Schools: LBS '21 Anderson '21
Posts: 68
Kudos: 116
 [2]
Through a point on the hypotenuse of a right triangle, lines are drawn 12 Apr 2019, 04:48
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is


(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)
Show more

Please find the image attached.
\(\triangle ABD\) and \(\triangle DEF\) are similar

So AB/DE = BD/EF

So \(\frac{x}{1}\)=\(\frac{1}{2m}\)
x= \(\frac{1}{2m}\)

Area of \(\triangle ABD\) = \(\frac{x}{2}\) =\(\frac{1}{4m}\)

So the ratio of \(\triangle ABD\) to area of Square BCDE to is = \(\frac{1}{4m}\)

ajmekal Sanjeetgujrall Hope this helps
Attachments

solution.JPG
solution.JPG [ 21.59 KiB | Viewed 5382 times ]

User avatar
Sanjeetgujrall
User avatar
Joined: 04 Sep 2016
Last visit: 26 Apr 2024
Posts: 50
Own Kudos:
62
Given Kudos: 66
Location: Germany
GPA: 3
Posts: 50
Kudos: 62
Through a point on the hypotenuse of a right triangle, lines are drawn 12 Apr 2019, 05:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Manas1212
Bunuel
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is


(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)

Please find the image attached.
\(\triangle ABD\) and \(\triangle DEF\) are similar

So AB/DE = BD/EF

So \(\frac{x}{1}\)=\(\frac{1}{2m}\)
x= \(\frac{1}{2m}\)

Area of \(\triangle ABD\) = \(\frac{x}{2}\) =\(\frac{1}{4m}\)

So the ratio of \(\triangle ABD\) to area of Square BCDE to is = \(\frac{1}{4m}\)

ajmekal Sanjeetgujrall Hope this helps
Show more

Hi mamas, how are they similar ?
Both have 1 side equal because of square and angle ABC = angle DEF....what's the third thing ?

Posted from my mobile device
User avatar
Manas1212
User avatar
Joined: 31 Jul 2017
Last visit: 10 Aug 2019
Posts: 68
Own Kudos:
116
 [1]
Given Kudos: 474
Location: India
Schools: LBS '21 Anderson '21
Schools: LBS '21 Anderson '21
Posts: 68
Kudos: 116
 [1]
Through a point on the hypotenuse of a right triangle, lines are drawn 12 Apr 2019, 07:00
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sanjeetgujrall
Manas1212
Bunuel
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is


(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)

Please find the image attached.
\(\triangle ABD\) and \(\triangle DEF\) are similar

So AB/DE = BD/EF

So \(\frac{x}{1}\)=\(\frac{1}{2m}\)
x= \(\frac{1}{2m}\)

Area of \(\triangle ABD\) = \(\frac{x}{2}\) =\(\frac{1}{4m}\)

So the ratio of \(\triangle ABD\) to area of Square BCDE to is = \(\frac{1}{4m}\)

ajmekal Sanjeetgujrall Hope this helps

Hi mamas, how are they similar ?
Both have 1 side equal because of square and angle ABC = angle DEF....what's the third thing ?

Posted from my mobile device
Show more

Take any angle as y , other angle of the triangle would be 90-y. So it would be angle-angle-angle Similar

Hope it helps

P.S It's Manas
avatar
georgethomps
avatar
Joined: 07 Mar 2019
Last visit: 28 Jul 2025
Posts: 21
Own Kudos:
14
Given Kudos: 2
Posts: 21
Kudos: 14
Through a point on the hypotenuse of a right triangle, lines are drawn 12 Apr 2019, 10:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Manas1212
Bunuel
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is


(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)

Please find the image attached.
\(\triangle ABD\) and \(\triangle DEF\) are similar

So AB/DE = BD/EF

So \(\frac{x}{1}\)=\(\frac{1}{2m}\)
x= \(\frac{1}{2m}\)

Area of \(\triangle ABD\) = \(\frac{x}{2}\) =\(\frac{1}{4m}\)

So the ratio of \(\triangle ABD\) to area of Square BCDE to is = \(\frac{1}{4m}\)

ajmekal Sanjeetgujrall Hope this helps
Show more
How are you deriving 2m?
User avatar
Sanjeetgujrall
User avatar
Joined: 04 Sep 2016
Last visit: 26 Apr 2024
Posts: 50
Own Kudos:
62
Given Kudos: 66
Location: Germany
GPA: 3
Posts: 50
Kudos: 62
Through a point on the hypotenuse of a right triangle, lines are drawn 12 Apr 2019, 11:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
georgethomps
Manas1212
Bunuel
Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is


(A) 1/(2m + 1)

(B) m

(C) 1 - m

(D) 1/(4m)

(E) 1/(8m^2)

Please find the image attached.
\(\triangle ABD\) and \(\triangle DEF\) are similar

So AB/DE = BD/EF

So \(\frac{x}{1}\)=\(\frac{1}{2m}\)
x= \(\frac{1}{2m}\)

Area of \(\triangle ABD\) = \(\frac{x}{2}\) =\(\frac{1}{4m}\)

So the ratio of \(\triangle ABD\) to area of Square BCDE to is = \(\frac{1}{4m}\)

ajmekal Sanjeetgujrall Hope this helps
How are you deriving 2m?
Show more

Its given the area of the square to one of the triangles is m. lets assume thats \(\triangle DEF\)

\(\frac{Area of triangle DEF}{Area of Square}\) = \(\frac{m}{1}\)

\(\frac{1/2*DE*AB}{1}\)= \(\frac{m}{1}\) where DE = 1


Solving this AB = 2m

georgethomps Hope that helps
User avatar
Sanjeetgujrall
User avatar
Joined: 04 Sep 2016
Last visit: 26 Apr 2024
Posts: 50
Own Kudos:
62
Given Kudos: 66
Location: Germany
GPA: 3
Posts: 50
Kudos: 62
Through a point on the hypotenuse of a right triangle, lines are drawn 12 Apr 2019, 12:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Manas1212

Actually that will not work. If we take any angle as y , other angle of the triangle would be 90-y.......agree

But it does not have to be the same for the other triangle. Other triangle could have an angle z and 90-z

But y does not have to be z

How is it AAA?
User avatar
Manas1212
User avatar
Joined: 31 Jul 2017
Last visit: 10 Aug 2019
Posts: 68
Own Kudos:
116
 [1]
Given Kudos: 474
Location: India
Schools: LBS '21 Anderson '21
Schools: LBS '21 Anderson '21
Posts: 68
Kudos: 116
 [1]
Through a point on the hypotenuse of a right triangle, lines are drawn 12 Apr 2019, 18:58
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sanjeetgujrall
Manas1212

Actually that will not work. If we take any angle as y , other angle of the triangle would be 90-y.......agree

But it does not have to be the same for the other triangle. Other triangle could have an angle z and 90-z

But y does not have to be z

How is it AAA?
Show more

Let \(\angle BAD\)= y

So \(\angle ADB\)=90-y= \(\angle DFE\)

Hope It Helps Sanjeetgujrall
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,991
Own Kudos:
1,118
Posts: 38,991
Kudos: 1,118
Through a point on the hypotenuse of a right triangle, lines are drawn 02 Aug 2023, 07:04
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.
Moderators:
Bunuel
Math Expert
109910 posts
Krunaal
Tuck School Moderator
852 posts