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What is the area of triangle AEC?

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by AAPL » Mon Nov 27, 2017 7:54 am
Image

In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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by Jay@ManhattanReview » Mon Nov 27, 2017 8:55 pm
AAPL wrote:Image

In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC?

A. 18
B. 13.5
C. 9
D. 4.5
E. 3

The OA is D.

Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
Note that ∆ABE and ∆CDE are similar. /_ABE = /_CDE; /_ABE = /_ECD; and /_AEB = /_CED

This implies that the ratio of corresponding sides for the triangles are equal

=> CD/AB = ED/AE
= 9/3 = ED/AE
= 3 = ED/AE => 3*AE = ED.

Now, since AD = AE + ED = 4, then AE + 3.AE = 4 => AE = 1 (and ED = 3).

The area of /_AEC = 1/2*(Base)*(Height) = AE*CD = (1/2)*1*9 = 4.5.

The correct answer: D

Hope this helps!

-Jay
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