Find the sides of the rectangle if its area is 117 cm² and the perimeter is 44 cm.

Rectangle, its area is 117 cm. 2, perimeter is 44 cm.

Find the sides of the rectangle a and b.

Solution. The area of the rectangle is calculated using the formula, S = a * b, and the perimeter, P = 2 * (a + b).

By the condition of the problem, a * b = 117, a + b = 22; a = → (22 – b) * b = 117, find the roots of the quadratic equation:

b ^ 2 – 22b + 117 = 0, D = 484 – 468 = 16.b1,2 = (22 ± √16) / 2, b1 = (22 + 4/2 = 13, b2 = (22 – 4) / 2 = 9.a1 = 22 – 13 = 9, a2 = 22 – 9 = 13.

Answer. 9, 13.