# The area of the rectangle is 40 cm2, and its perimeter is 26 cm. What are the length and width of the rectangle?

January 16, 2021 | education

| To begin with, we recognize half of the perimeter, which is the length and width of the rectangle. Divide the perimeter by 2.

p = 26 cm ÷ 2 = 13 cm.

To solve the problem, let’s designate the length of the rectangle as x, then the width will be 13 cm – x. The product of length and width will be equal to the area. Let’s compose and solve the equation.

x * (13 – x) = 40.

13 * x – x² = 40.

-13 * x + x² = – 40.

x² – 13 * x + 40 = 0.

D = 169 – 160 = 9.

x1 = (13 + 3) ÷ 2 = 8.

x2 = (13 – 3) ÷ 2 = 5.

Answer: the length of the rectangle is 8 cm, the width is 5 cm.