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:
Answer Choices:
A. K must be an integer.
B. K must be a rational fraction
C. K must be an irrational number
D. K must be an integer or a rational fraction
E. taken alone neither (A) nor (B) nor (C) nor (D) is true
Solution:
The shorter base, the altitude, and the longer base may be represented by a , , and , respectively. . Since may be the square of an integer, a non-square integer, the square of a rational fraction, a non-square rational fraction, or irrational, the correct choice is ( E ).