Asked by Curtis
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?
Answers
Answered by
Steve
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
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
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