Let ∠ABD = x and ∠BDA = y, implying that x+y = 90.
The result is the following figure:
Every triangle in the figure above has the same combination of angles:
x-y-90.
Implication:
All of the triangles are SIMILAR.
Corresponding sides in similar triangles are in the SAME RATIO.
Since AB=15 and AD=20, ∆ABD is a multiple of a 3-4-5 triangle:
AB:AD:BD = 3:4:5 = 15:20:25.
Since ∆BCE is similar to ∆ABD, ∆BCE must also be a multiple of a 3-4-5 triangle.
Since BC=20, we get:
CE:BE:BC = 3:4:5 = 12:16:20.
Thus, CE=12 and BE=16, implying that the area of ∆BCE = (1/2)(BE)(CE) = (1/2)(16)(12) = 96.
The correct answer is
C.
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
