In the figure, AB||CB. If CD:BA = 6:5 and the area of CED is 288, find the area of BEA

Accepted Solution

Since AB and CD are parallel, and they intersect, the smaller triangle is similar to the large. They will have the same ratio of sides and congruent angles. Thus, their bases are in a ratio and their heights should be in the same ratio, and their areas will be proportional.
Area of large triangle:
1/2 bh = 1/2 (6)6x = 288
18x = 288
x = 16 = ratio factor to be applied to smaller
So now the small triangle is:
1/2 (5)(5x) = (25/2)x = (25/2)(16) = 25Γ—8 = 200