Problem: In triangle ABC, with AB=AC=3.6, a point D is taken on AB at a distance 1.2 from A. Point D is joined to point E in the prolongation of AC so that triangle AED is equal in area to triangle ABC. Then AE equals:
Answer Choices:
A. 4.8
B. 5.4
C. 7.2
D. 10.8
E. 12.6
Solution:
Let the altitude from B to AC be h. Then the altitude from D to AE is 31βhβ. Let AE=xΛ. Then
21ββ
31βhx=21βh(3.6)β΄x=10.8