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

| May 26, 2021 | education

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

Let x denote the length of the first side of this quadrangle.

According to the condition of the problem, the first side of this quadrangle is 5 cm less than its second side, therefore, the length of the second side of this quadrangle is x + 5 cm.

Also, according to the condition of the problem, the second side of this quadrangle is 6 cm larger than the third side, therefore, the length of the third side of this quadrangle is x + 5 – 6 = x – 1 cm.

Also, according to the condition of the problem, the fourth side of this quadrangle is 2 times larger than the third side, therefore, the length of the fourth side of this quadrangle is 2 * (x – 1) cm.

Also, according to the condition of the problem, the perimeter of this quadrangle is 27 cm, therefore, we can draw up the following equation:

x + x + 5 + x – 1 + 2 * (x – 1) = 27.

We solve the resulting equation:

x + x + 5 + x – 1 + 2x – 2 = 27;

5x + 2 = 27;

5x = 27 – 2;

5x = 25;

x = 25/5;

x = 5 cm.

Knowing the length of the first side of this quadrangle, we find the lengths of its three other sides:

x + 5 = 5 + 5 = 10 cm;

x – 1 = 5 – 1 = 4 cm;

2 * (x – 1) = 2 * 4 = 8 cm.

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



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