Geometry

Hi Rich ,

Can you pls solve this?

I am using the same concept but not getting answer.

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.