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smc

geometry senior

Problem

A rectangle inscribed in a triangle has its base coinciding with the base of the triangle. If the altitude of the triangle is , and the altitude of the rectangle is half the base of the rectangle, then:
(A)
(B)
(C)
(D)
Solution
Draw the triangle.The small triangle formed by taking away the rectangle and the two small portions left is similar to the big triangle.Hence, the proportions of the heights is equal to the proportions of the sides. In particular, we get The answer is .
Final answer
C