The sum of two adjacent sides of the rectangle is 27 cm. Find the sides of the rectangle, knowing that its area is 180 cm2.

We denote by a the length of one of the adjacent sides of this rectangular quadrangle.

Since the sum of two adjacent sides of this rectangular quadrangle is 27 cm, the length of its second adjacent side is 27 – a cm.

According to the condition of the problem, the area of ​​this rectangular quadrangle is 180 cm2, therefore, we can draw up the following equation:

a * (27 – a) = 180,

solving which, we get:

27a – a ^ 2 = 180;

a ^ 2 – 27a + 180 = 0;

a = (27 ± √ (729 – 4 * 180)) / 2 = (27 ± √9) / 2 = (27 ± 3) / 2;

a1 = (27 + 3) / 2 = 30/2 = 15 cm;

a2 = (27 – 3) / 2 = 24/2 = 12cm.

We find the second side.

With a = 15 cm:

27 – 15 = 12 cm.

With a = 12 cm:

27 – 12 = 15 cm.

Answer: the lengths of the sides are 15 cm and 12 cm.