# 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.

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