# The rectangle has a perimeter of 12.2 and an area of 9.1. Determine the sides of the rectangle.

March 29, 2021 | education

| We denote the sides of the rectangle through a and b.

The perimeter equals:

2a + 2b = 12.2;

The area is equal to:

a * b = 9.1

In the expression a * b = 9.1, we express in through a:

b = 9.1 / a;

Substitute the expressed value into the first expression and find a:

2a + 2 * 9.1 / a = 12.2;

2a ^ 2 + 18.2 = 12.2 a;

2a ^ 2 – 12.2a + 18.2 = 0;

a ^ 2 – 6.1a + 9.1 = 0

We solve the quadratic equation:

a 1.2 = (6.1 ± √37.21 – 4 * 9.1) / 2;

a 1.2 = (6.1 ± √0.81) / 2;

a 1 = (6.1 + 0.9) / 2 = 3.5;

a 2 = (6.1 – 0.9) / 2 = 2.6;

Find the value in:

in 1 = 9.1 / a = 9.1 / 3.5 = 2.6;

in 2 = 9.1 / 2.6 = 3.5.

Answer: a 1 = 3.5, in 1 = 2.6; a 2 = 2.6, b 2 = 3.5