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

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.