# Find the sides of a quadrilateral if the perimeter is 8cm, and one side is larger than each of the other

**Find the sides of a quadrilateral if the perimeter is 8cm, and one side is larger than each of the other sides by 3mm, 4mm, 5mm.**

The perimeter of a quadrilateral is the sum of the lengths of all its sides:

P = AB + BC + CD + AD.

Since the perimeter of the quadrangle is 8 cm, which corresponds to 80 mm, the BC side is 3 mm larger than AB, the CD side is 4 mm larger than BC, and the AD side is 5 mm larger than CD, we will express it as follows:

x is the length of the side AB;

x + 3 – the length of the BC side;

x + 3 + 4 is the length of the CD side;

x + 3 + 4 + 5 – side length AD.

x + x + 3 + x + 3 + 4 + x + 3 + 4 + 5 = 80;

x + x + x + x = 80 – 3 – 3 – 4 – 3 – 4 – 5;

4x = 58;

x = 58/4 = 14.5;

AB = 14.5 mm;

BC = 14.5 + 3 = 17.5 mm;

CD = 17.5 + 4 = 21.5 mm;

AD = + 21.5 = 26.5 mm.

Answer: the sides of the quadrangle are 14.5 cm, 17.5 cm, 21.5 cm, 26.5 cm.