If a square is divided into five congruent rectangles and the perimeter of one of the rectangles is 30centimeters what is the area of the square?

x y y y y y Perimeter of each rectangle = 2x + 2y = 30 which can be reduced: x + y = 15 Thus the perimeter of square = 2x + 10y Since it is a square: x = 5y Replacing values in equation: 2(5y) + 2y = 30 Solving for y: 10y + 2y = 30 : 12y = 30 : y = 2.5 Which means x = 12.5 Area of square = (12.5)2 = 156.25 cm2 Checking that numbers fit original: 2(12.5) + 2(2.5) = 25 + 5 = 30