Question

If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.

Answer 1

Let x represent the side length of the square. Then
  (x +4)*(x -5) +40 = x^2
  x^2 -x -20 +40 = x^2
  20 = x

The rectangle is 15 cm by 24 cm, and its area is 360 cm^2.