by decreasing each dimension by 2 units, the area of a rectangle decrease from 40 square feet (on left) to 16 square feet (on the right). find the percent decrease in area ---------------------- Draw a rectangle inside a rectangle. ------- Dimensions of the outer area are x and y Area = x*y = 40 sq. ft. --------------------------------------------------------- Dimensions of the inner rectangle are (x-2) and (y-2) Area = (x-2)(y-2) ------- Equations:: xy = 40 sq ft (x-2)(y-2) = 16 sq ft ----- xy -2x -2y + 4 = 16 Substitute for "xy" to get: 40 -2x -2y = 12
---- 2x + 2y = 28 x + y = 14 ---- Using x+y = 14 , substitute for "y" and solve for "x":: xy = 40 x(14-x) = 40 14x - x^2 = 40 x^2 - 14x + 40 = 0 Factor:: (x-10)(x-4) = 0 If x = 10, y = 4 If x = 4, y = 10
