Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 1808:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Posts: 4,475
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
71% (02:33) correct
29%
(03:01)
wrong
based on 191
sessions
History
Date
Time
Result
Not Attempted Yet
Attachment:
similar triangle diagram.JPG [ 15.8 KiB | Viewed 6334 times ]
(A) 175
(B) 350
(C) 775
(D) 1150
(E) 1575
For a set of practice problems on Similar Geometric Figures, as well as the OE for this particular problem, see:
https://magoosh.com/gmat/2014/gmat-pract ... c-figures/
Mike
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
These are similar triangles, but small one is reversed. After noticing that, question is easily solved by proportion:
AE/BD=AC/CD=8/1
40*10*8/2 (area of big triangle) - 5*10/2 = 1575
Answer E
AE/BD=AC/CD=8/1
40*10*8/2 (area of big triangle) - 5*10/2 = 1575
Answer E
beattheheat
Joined: 20 Feb 2013
Last visit: 08 Aug 2022
Posts: 66
Location: India
Schools: IIMA (D) SPJ PGPM"16 (A)
GMAT 1: 690 Q49 V34
WE:Information Technology (Computer Software)
Triangle BCD is similar to Triangle ACE having one right angle and one common angle.
Ratio of sides is 1:8, thus ratio of Area will be 1:64.
Area of BCD = (5*10)/2= 25
Area of ACE = 64*(Area of BCD) = 64*25 = 1600
Area of shaded region = Area of ACE - Area of BCD = 1600 - 25 = 1575
Answer E
Ratio of sides is 1:8, thus ratio of Area will be 1:64.
Area of BCD = (5*10)/2= 25
Area of ACE = 64*(Area of BCD) = 64*25 = 1600
Area of shaded region = Area of ACE - Area of BCD = 1600 - 25 = 1575
Answer E
Schools: Darden '21
Posts: 10
How do you know that Two triangles are in ratio 1 to 8? If you take CD to be as like side with AE, the two triangles will be in ratio 1 to 4.
IMO E
As the two trinagles are similar
(area of big triangle x )/(area of small triangle y) = (ratio of corresponding sides)^2
x/25 = (8/1)^2
x = 64*25 = 1600
so area of shaded region = 1600-25 = 1575
Award kudos if helpful
Posted from my mobile device
As the two trinagles are similar
(area of big triangle x )/(area of small triangle y) = (ratio of corresponding sides)^2
x/25 = (8/1)^2
x = 64*25 = 1600
so area of shaded region = 1600-25 = 1575
Award kudos if helpful
Posted from my mobile device
Posts: 4
how do you conclude that they are similar triangles ? because either its SAS, AAA or SSS but here from the given question we know only one angle is equal? kindly help.
BDC=CAE ( both are 90*), BCD=ACE (common angle in 2 triangles)
Obviously remaining angles gonna be equal.
Obviously remaining angles gonna be equal.
TannyaChabbra
Posts: 1,324
Triangle CAE ~ Triangle CDB
(by the A-A Postulate)
Ratio of Corresponding Sides:
Triangle CAE : Triangle CDB = Side AE : Side DB = 40 : 5 = 8 : 1
RATIO of Areas of Similar Triangles = SQUARE of the Ratio of Corresponding Sides in its most reduced form
AREA of Triangle CAE : AREA of Triangle CDB = (8)^2 : (1)^2 = 64 : 1
Actual Area of Triangle CDB = (1/2) * 5 * 10 = 25
Given the Ratio of Areas ----> Actual Area of Triangle ACE = 25 * (64) = 1, 600
Shaded Area = Area of Triangle ACE - Area of Triangle CDB = 1,600 - 25 =
1,575
-E-
(by the A-A Postulate)
Ratio of Corresponding Sides:
Triangle CAE : Triangle CDB = Side AE : Side DB = 40 : 5 = 8 : 1
RATIO of Areas of Similar Triangles = SQUARE of the Ratio of Corresponding Sides in its most reduced form
AREA of Triangle CAE : AREA of Triangle CDB = (8)^2 : (1)^2 = 64 : 1
Actual Area of Triangle CDB = (1/2) * 5 * 10 = 25
Given the Ratio of Areas ----> Actual Area of Triangle ACE = 25 * (64) = 1, 600
Shaded Area = Area of Triangle ACE - Area of Triangle CDB = 1,600 - 25 =
1,575
-E-
Posts: 1,324
I find it easier to remember the A-A-A Postulate to prove Triangle Similarity as just the
A-A Postulate
if 2 Angles are Equal across 2 Triangles ------> the 3rd Corresponding Angle will be Equal also and the Triangles will be Similiar
A-A Postulate
if 2 Angles are Equal across 2 Triangles ------> the 3rd Corresponding Angle will be Equal also and the Triangles will be Similiar
TannyaChabbra
Posts: 107
Triangle ACE is similar to triangle BCD.
Attachments
File comment: Pfa
A871C650-05C1-430A-BD5A-ED4D167B2A06.jpeg [ 816.66 KiB | Viewed 1793 times ]
Moderator:
Announcements
Monday, Sep 14, 2026
11:30am NY / 3:30pm London / 9pm Mumbai
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.