Find the perimeter of a rectangle that is 4 cm longer than wide and has

Find the perimeter of a rectangle that is 4 cm longer than wide and has an area of 60 cm2? Find three consecutive integers whose sum of squares is 869?

a) Let’s denote the width of the rectangle as x, and the length x + 4 cm. The product of the length and width is equal to the area, which is 60 cm². Let’s make an equation.

x * (x + 4) = 60.

x² + 4 * x – 60 = 0.

D = 16 + 240 = 256.

x1 = (-4 + 16) ÷ 2 = 6.

x2 = (-4 – 16) ÷ 2 = -10.

The width is 6 cm, the length is 10 cm. Find the perimeter.

P = (6 cm + 10 cm) * 2 = 32 cm.

b) By the selection method, 3 numbers were determined whose sum of squares is 869.

16² + 17² + 18² = 256 + 289 + 324 = 869.

Answer: a) the perimeter is 32 cm, b) the numbers 16, 17, 18.