# Find the sides of the quadrilateral, if its perimeter is 27 cm, the first side is 5 cm less than the second

**Find the sides of the quadrilateral, if its perimeter is 27 cm, the first side is 5 cm less than the second, the second is 6 cm more than the third, and the fourth is 2 times larger than the third.**

We denote by x the length of the third side of this quadrilateral.

According to the condition of the problem, the second side of this quadrangle is 6 cm larger than the third, and the fourth side is 2 times larger than the third, therefore, the lengths of the second and fourth sides of the quadrilateral are, respectively, x + 6 cm and 2x cm.

It is also known that the first side is 5 cm less than the second, therefore, the length of the first side of the quadrangle is x + 6 – 5 = x + 1 cm.

By the condition of the problem, the perimeter of this quadrilateral is 27 cm, therefore, we can draw up the following equation:

x + 1 + x + 6 + x + 2x = 27.

We solve the resulting equation:

5x + 7 = 27;

5x = 27 – 7;

5x = 20;

x = 4 cm.

Find the lengths of the first, second and fourth sides:

x + 1 = 4 + 1 = 5 cm;

x + 6 = 4 + 6 = 10 cm;

2x = 2 * 4 = 8 cm.

Answer: the lengths of the sides of this quadrilateral are 5 cm, 10 cm, 4 cm and 8 cm.