BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Which is the height of the parallelogram and the triangle?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pm
Thanked: 11 times
Followed by:8 members

Which is the height of the parallelogram and the triangle?

by gmattesttaker2 » Sat Nov 23, 2013 11:03 am
Hello,

For this problem:

In parallelogram ABCD, point E lies on side AD. If the area of the parallelogram
is three times the area of triangle ABE,what is the ratio of the length of AE to
the length of AD?


If I draw the following parallelogram (shown in the attachment) would AB be the height of parallelogram ABCD as well as triangle ABE?


Thanks,
Sri
Attachments
Parallelogram.png
Parallelogram
Top
Source: — Problem Solving |
User avatar
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Thu Sep 26, 2013 9:05 pm
Thanked: 5 times

by riz_gmat » Sat Nov 23, 2013 12:11 pm
If we join diagonal BD of parallelogram ABCD , we get another triangle ABD, such that
Area of || gram ABCD = 2 Area of tri (ABD) ( since both have same base and lie bet same parallel lines) ---- 1
Area of || gram ABCD = 3 Area of tri (ABE) (Given in the question)---- 2

From 1 & 2,
2 Area of tri (ABD) = 3 Area of tri (ABE)
ie, Area of tri (ABE) / Area of tri (ABD) = 2 / 3

tri (ABE) and tri (ABD) are Similar triangles (AA Test of similarity)

Hence , Area of tri (ABE) / Area of tri (ABD) = (AE)^2 / (AD)^2 = 2/3
Therefore, [spoiler]AE / AD = sqaure root of ( 2 / 3)[/spoiler]
whatz the answer?
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Nov 23, 2013 2:53 pm
gmattesttaker2 wrote: In parallelogram ABCD, point E lies on side AD. If the area of the parallelogram
is three times the area of triangle ABE, what is the ratio of the length of AE to
the length of AD?
Image

ABCD can be ANY type of parallelogram.

ABCD:
Let ABCD be a square where s=3.
Area of square ABCD = s² = 3² = 9.

∆ABE:
Since the area of square ABCD is 3 times the area of ∆ABE, the area of ∆ABE = 3.
Thus:
(1/2)(AE)(AB) = 3
(1/2)(AE)(3) = 3
AE = 2.

Resulting ratio:
AE : AD = 2:3.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1