If the length of the rectangle is reduced by 4cm, and the width is increased by 5cm

If the length of the rectangle is reduced by 4cm, and the width is increased by 5cm, you will get a square whose area is 40cm2 larger than the area of the rectangle. Find the area of a rectangle?

1. We take the length of the rectangle for x, for its width.
2. The area of the rectangle is xy cm ^ 2.
3. The area of the square is (x – 4) (y + 5) cm ^ 2.
4. Let’s compose two equations:
(x – 4) (y + 5) – xy = 40; xy + 5x – 4y – 20 – xy = 40; 5x – 4y = 60;
(x – 4) = (y + 5;) x – y = 9;
5. Multiply the second equation by 5:
5x – 5y = 45;
6. Subtract this equation from the first:
5x – 5x – 4y + 5y = 15; y = 15;
x = 15 + 9 = 24.
7. The area of the rectangle is 15 x 24 = 360 cm ^ 2.
Answer: The area of the rectangle is 360 cm ^ 2.