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Answer :
The longer side of the rectangle, which has an area of 20 square inches and a perimeter equivalent to a square with an area of 36 square inches, is 10 inches.
To find the length of the longer side of the rectangle WXYZ, we first need to find the side length of the square ABCD. Since the area of a square is calculated as side length squared, and the area of square ABCD is 36 square inches, the side length of square ABCD is 6 inches (since 6 squared equals 36). Next, we know the two shapes have equal perimeters. The perimeter of a square is calculated as 4 times the side length, so the perimeter of square ABCD is 24 inches. A rectangle's perimeter is calculated as 2 times the length plus 2 times the width. Since the rectangle WXYZ has the same perimeter as ABCD, 2 times the length plus 2 times the width is also 24 inches.
The area of rectangle WXYZ is 20 square inches, so the width of rectangle WXYZ is the area divided by the length. In order to maximize the area, the width of the rectangle should be less than the length. Hence, by process of elimination, the length of rectangle WXYZ should be 10 inches, resulting in a width of 2 inches (since 10 times 2 equals the 20 square inches area of rectangle WXYZ).
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