# The sum of the lengths of all sides of the quadrilateral is 66 dm. Find the length of each side, knowing

**The sum of the lengths of all sides of the quadrilateral is 66 dm. Find the length of each side, knowing that these lengths are equal to consecutive numbers.**

If the lengths of the sides are consecutive numbers. so they differ from each other by 1, for example: 10, 11 = 10 +1, 12 = 10 + 2, 13 = 10 + 3.

Let the length of the first side be x dm, then the length of the second side is (x + 1) dm, the length of the third side is (x + 2) dm and the fourth is (x + 3). The sum of all sides of the quadrangle is (x + (x + 1) + (x + 2) + (x + 3)) dm or 66 dm. Let’s make an equation and solve it.

x + (x + 1) + (x + 2) + (x + 3) = 66;

x + x + 1 + x + 2 + x + 3 = 66;

4x + 6 = 66;

4x = 66 – 6;

4x = 60;

x = 60: 4;

x = 15 (dm) – the first side;

15 + 1 = 16 (dm) – the second side;

15 + 2 = 17 (dm) – third party;

15 + 3 = 18 (dm) – the fourth side.

Answer. 15 dm, 16 dm, 17 dm, 18 dm.