AAPL wrote:
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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