The perimeter of the rectangle is 20cm. Find its sides if you know that the area of the rectangle is 24cm ^ 2

The solution of the problem.

1. Let’s denote the width of the rectangle through x.

2. Determine the length of the rectangle

((20/2) – x) = (10 – x) cm.

3. Let’s compose and solve the equation.

x * (10 – x) = 24;

10x – x ^ 2 = 24;

– x ^ 2 + 10x – 24 = 0;

D = 10 ^ 2 – 4 * (- 1) * (- 24) = 100 – 96 = 4;

x1 = (- 10 + 2) / (2 * (- 1)) = – 8 / (- 2) = 4;

x2 = (- 10 – 2) / (2 * (- 1)) = – 12 / (- 2) = 6.

4. The width of the rectangle is x = 4 cm.

5. How long is the rectangle?

10 – 4 = 6 cm.

Answer: the width of the rectangle is 4 cm, the length of the rectangle is 6 cm.