+1911 The area of square $ABCD$ is 36 square inches. The area of rectangle $WXYZ$ is 24 square inches. If the two shapes have equal perimeters, what is the length of the longer side of rectangle $WXYZ$?
+129895 Side of square = 6
Perimeter = 24
Area of rectangle = x * y = 24
Perimeter of rectangle 2 ( x + y) = 24
So x + y = 12
So y = 12 - x
So
x ( 12 -x) = 24
-x^2 + 12x =24
x^2 - 12x + 24 = 0 complete the square on x
x^2 -12x + 36 = -24 + 36
(x -6)^2 = 12 take the positive root
x - 6 = sqrt (12)
x = 6 + sqrt (12) = 6 + 2sqrt (3) = longer side of rectangle
