The perimeter of the triangle is 117 cm. Find its sides if one of them is 7 cm larger

| May 2, 2021 | education

The perimeter of the triangle is 117 cm. Find its sides if one of them is 7 cm larger than the other and 19 cm less than the third.

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

According to the condition of the problem, the first side of this triangle is 7 cm larger than its other side and 19 cm less than the third side of this triangle, therefore, the lengths of the second and third sides of this triangle are, respectively, x – 7 cm and x + 19 cm.

It is also known that the perimeter of this triangle is 117 cm, therefore, we can draw up the following equation:

x + x – 7 + x + 19 = 117.

We solve the resulting equation and find the length of the first side of this triangle:

3x + 12 = 117;

3x = 117 – 12;

3x = 105;

x = 105/3;

x = 35 cm.

Knowing the length of the first side of a given triangle, we find the lengths of its other two sides:

x – 7 = 35 – 7 = 28 cm;

x + 19 = 35 + 19 = 54 cm.

Answer: the lengths of the side of this triangle are 35 cm, 28 cm and 54 cm



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