Specify the size of the sides of the rectangle if its area is 12 square meters. cm, and the perimeter is 26 cm.

Since the perimeter is twice the sum of the sides of the rectangle, then the sum of its sides will be:

26/2 = 13 cm.

This value can be decomposed into the following parts.

1 + 12 = 13 cm.

2 + 11 = 13 cm.

3 + 10 = 13 cm.

And so on.

Since the area of the rectangle is the product of its sides, the width will be 1 cm and the length will be 12 cm.

1 * 12 = 12 cm2

Solution through the system.

x + y = 13.

x * y = 12.

x = 13 – y.

(13 – y) * y = 12.

13 * y – y ^ 2 = 12.

y ^ 2 – 13 + 12 = 0.

D ^ 2 = 13 * 13 – 4 * 1 * 12 = 169 – 48 = 121.

D = √121 = 11.

x = (13 + 11) / 2 = 12 cm (length).

13 – 12 = 1 cm (width).

Answer: 1 and 12 cm.