+1932 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?
+130477 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
