In the figure, AB||CB. If CD:BA = 6:5 and the area of CED is 288, find the area of BEA
Accepted Solution
A:
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. 5b1:6b2 5h1:6b2 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) = 25×8 = 200