The area of the rectangle is 36 cm2, the perimeter is 30 cm, what are the sides of the rectangle?

The perimeter of a rectangle is twice the sum of its sides, so the sum of the length and width of the shape will be:

30/2 = 15 cm.

We draw up an equation in which we write the length of the rectangle as the unknown value of x.

In this case, the width of the rectangle will be: 15 – x cm.

The area of a rectangle is the product of its sides, so it will be:

x * (15 – x) = 36.

15 * x – x ^ 2 = 36.

x ^ 2 – 15 * x + 36 = 0.

D ^ 2 = (-15) ^ 2 – 4 * 1 * 36 = 225 – 144 = 81.

√D = √81 = 9.

x = (15 – 9) / 2 = 6/2 = 3 cm (length).

15 – x = 15 – 3 = 12 cm (width).

Checking the solution:

S = 12 * 3 = 36 cm2

Answer: 12 and 3 cm.