Isosceles triangle $ABE$ of area 100 square inches is cut by $\overline{CD}$ 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 $\overline{CD}$?

Answer 1

Let AF be the altitude from A to BE
Let M be the midpoint of CD (lies on AF)
∆ACD has 1/4 the area of ∆ABE
so, since ACD ~ ABE, CD = 1/2 BE and AM = 1/2 AF

BE*AF/2 = 100
BE=200/20 = 10
so, CD = 5

Answer 2

stop cheating

Answer 3

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Answer 4

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