Bunuel wrote:
A parallelogram has perimeter 16 and base of length 5. Which of the following could NOT be the area of the parallelogram?
(A) 20
(B) 15
(C) 10
(D) 4
(E) 1
Since a parallelogram has two sets of equal-length opposite sides, we have:
2a + 2b = perimeter
2a + 2(5) = 16
2a = 6
a = 3
The two adjacent sides, i.e., the two sides that have different lengths, are 5 and 3. Even if these two sides are perpendicular, i.e., the parallelogram is a rectangle, the area is at most 5 x 3 = 15. If they are not perpendicular, the area would be less than 15. Therefore, the area of the parallelogram can’t be 20 since the area can’t be more than 15.
Answer: A
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