ExplanationBecause the length of each side of rectangle R is an integer and each length is a factor of the area 36, there are 5 possible rectangles: a 1 × 36 rectangle, a 2 × 18 rectangle, a 3 x 12 rectangle, a 4 × 9 rectangle, and a 6 × 6 rectangle.
The perimeter of the 1 × 36 rectangle is 2(1 + 36), or 74.
The perimeter of the 2 × 18 rectangle is 2(2 + 18), or 40.
The perimeter of the 3 × 12 rectangle is 2(3 + 12), or 30.
The perimeter of the 4 × 9 rectangle is 2(4 + 9), or 26.
The perimeter of the 6 × 6 rectangle is 2(6 + 6), or 24.
Since each of the 5 possible rectangles has a different perimeter, Quantity A, the number of possible values of the perimeter, is 5. Since Quantity B is 6, the correct answer is
Choice B.
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