Find the length and width of the rectangle if the width of the rectangle is 3 cm less than the length, and the area is 40 cm2.

Let the width of the rectangle be x cm, then the length of the rectangle is (x + 3) cm.It is known that the area of the rectangle is (the area of the rectangle is equal to the product of the length by the width) x (x + 3) cm ^ 2 or 40 cm ^ 2. Let’s make an equation and solve it.

x (x + 3) = 40;

x ^ 2 + 3x – 40 = 0;

D = b ^ 2 – 4ac;

D = 3 ^ 2 – 4 * 1 * (- 40) = 9 + 160 = 169; √D = 13;

x = (- b ± √D) / (2a);

x1 = (- 3 + 13) / (2 * 1) = 10/2 = 5 (cm) – width;

x2 = (- 3 – 13) / 2 = – 16/2 = – 8 – side length cannot be expressed as a negative number.

5 + 3 = 8 (cm) – length.

Answer. 5 cm, 8 cm.