The area of a rectangle, one side of which is 4 cm larger than the other, is 32 cm2.

The area of a rectangle, one side of which is 4 cm larger than the other, is 32 cm2. Find the sides and perimeter of the rectangle.

Let one side of the rectangle be x cm, then the second side of the rectangle is (x + 4) cm (if … more, then you need to add). The area of ​​a rectangle is equal to the product of its sides, i.e. x (x + 4) cm ^ 2 or 32 cm ^ 2. Let’s make an equation and solve it.

x (x + 4) = 32;

x ^ 2 + 4x = 32;

x ^ 2 + 4x – 32 = 0;

D = b ^ 2 – 4ac;

D = 4 ^ 2 – 4 * 1 * (-32) = 16 + 128 = 144; √D = 12;

x = (-b ± √D) / (2a);

x1 = (-4 + 12) / 2 = 8/2 = 4 (cm) – one side;

x2 = (-4 – 12) / 2 = -16/2 = -8 – length cannot be negative;

x + 4 = 4 + 4 = 8 (cm) – the second side.

Find the perimeter of the rectangle. The perimeter of a rectangle is equal to the sum of the lengths of its sides. P = 2 (a + b).

P = 2 (4 + 8) = 2 * 12 = 24 (cm).

Answer. 4 cm, 8 cm, P = 24 cm.