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smc

geometry intermediate

Problem

Let , in square units, be the area of a trapezoid such that the shorter base, the altitude, and the longer base, in that order, are in arithmetic progression. Then:
(A)
(B)
(C)
(D)
(E)
Solution
From the problem we can set the altitude equal to , the shorter base equal to , and the longer base equal to . By the formula for the area of a trapezoid, we have . However, since can equal any real number , none of the statements need to be true, so the answer is .
Final answer
E