Find the sides of the spruce quadrangle if its perimeter is 66 cm, the first side is 8 cm larger

Find the sides of the spruce quadrangle if its perimeter is 66 cm, the first side is 8 cm larger than the second and by the same amount less than 3 sides and 4 is 3 times more than 2.

We denote by x the length of the second side of the quadrilateral.

According to the condition of the problem, the first side is 8 cm larger than the second side, therefore, the length of the first side is x + 8 cm.

It is also known that the first side is 8 cm less than the third side, therefore, the length of the third side is x + 8 + 8 = x + 16 cm.

It is also known that the fourth side is 3 times larger than the second, therefore, the length of the fourth side is 3 cm.

By the condition of the problem, the perimeter of the quadrangle is 66 cm, therefore, we can draw up the following equation:

x + 8 + x + x + 16 + 3x = 66.

We solve the resulting equation:

6x + 24 = 66;

6x = 66 – 24;

6x = 42;

x = 42/6;

x = 7 cm.

Knowing the length of the second side, we find the length of the remaining sides:

x + 8 = 7 + 8 = 15 cm;

x + 16 = 7 + 16 = 23 cm;

3x = 3 * 7 = 21 cm.

Answer: the lengths of the sides of the quadrangle are 15 cm, 7 cm, 23 cm and 21 cm.