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

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

We denote the length of the first side of this triangle through x, the length of the second side of this triangle through y, the length of the third side of this triangle through z.

According to the condition of the problem, the first side of this triangle is 7 cm larger than its second side and 19 cm less than its third side, therefore, we can write the following ratios:

x = y + 7;

x = z – 19.

It is also known that the perimeter of this triangle is 117 cm, therefore, the following relationship holds:

x + y + z = 117.

We solve the resulting system of equations.

We express using the first equation y in terms of x, and using the second equation z in terms of x:

y = x – 7;

z = x + 19.

Substituting these values ​​for y and z in the equation x + y + z = 117, we get:

x + x – 7 + x + 19 = 117;

3x + 12 = 117;

3x = 117 – 12;

3x = 105;

x = 105/3;

x = 35 cm.

Knowing x, we find y and z:

y = x – 7 = 35 – 7 = 28 cm;

z = x + 19 = 35 + 19 = 54 cm.

Answer: the sides of this triangle are 35 cm, 28 cm and 54 cm.