Isosceles triangle ABE of area 100 square inches is cut by CD into an isosceles trapezoid and a smaller isosceles triangle. The area of the trapezoid is 75 square inches. If the altitude of triangle ABE from A is 20 inches, what is the number of inches in the length of CD?

Answer 1

since the area of ABE is 100, and the altitude is 20, the length of AB is 10.

Since the area of ABCD is 3/4 the area of ABE, CDE has 1/4 the area. So, CDE~ABE, with a scale factor of 1/2.

So, CD = AB/2 = 5

check: the altitude of ABCD is 1/2 * 20 = 10
the area of ABCD is thus (10+20)/2 * 5 = 75