In a triangle, one side is 8cm less than the other and 4cm less than the third.

In a triangle, one side is 8cm less than the other and 4cm less than the third. Find the lengths of the sides of the triangle if its perimeter is 54cm.

Let us denote the lengths of the sides of this triangle by x1, x2 and x3.

According to the condition of the problem, the first side of this triangle is less than the second side of this triangle by 8 cm and less than the third side by 4 cm, therefore, the following relations hold:

x2 = x1 + 8;

x3 = x1 + 4.

It is also known that the perimeter of this triangle is 54 cm, therefore, the following relationship holds:

x1 + x2 + x3 = 54.

Substituting into the last ratio the values ​​x2 = x1 + 8 and x3 = x1 + 4, we get:

x1 + x1 + 8 + x1 + 4 = 54;

3×1 + 12 = 54;

3×1 = 54 – 12;

3×1 = 42;

x1 = 42/3;

x1 = 14 cm.

Knowing x1, we find x2 and x3:

x2 = x1 + 8 = 14 + 8 = 22 cm;

x3 = x1 + 4 = 14 + 4 = 18 cm.

Answer: the lengths of the sides of the triangle are 14 cm, 22 cm and 18 cm.