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smc

geometry senior

Problem

Five rectangles, , , , , and , are arranged in a square as shown below. These rectangles have dimensions , , , , and , respectively. (The figure is not drawn to scale.) Which of the five rectangles is the shaded one in the middle?
problem
(A)
(B)
(C)
(D)
Solution
The area of this square is equal to , and thus its side lengths are . The sum of the dimensions of the rectangles are . Thus, because the perimeter of the rectangle is , the rectangle on the inside must have a perimeter of . The only rectangle that works is .
Final answer
B