# One side of an isosceles triangle is 8cm smaller than the other. Find the sides of this triangle if its perimeter is 44cm.

An isosceles triangle is a triangle in which the sides are equal:

AB = BC.

The perimeter of a triangle is the sum of the lengths of its sides:

P = AB + BC + AC.

In the first case, suppose the sides are 8 cm smaller than the base.

Thus, we express:

x is the length of the sides AB and BC;

x + 8 is the length of the AC base;

x + x + x + 8 = 44;

x + x + x = 44 – 8;

3x = 36;

x = 36/3 = 12;

AB = BC = 12 cm;

AC = 12 + 8 = 20 cm.

In the second case, suppose the base is 8 cm smaller than the sides.

Based on this, we express:

x is the length of the base of the speaker;

x + 8 – the length of the sides AB and BC;

x + x + 8 + x + 8 = 44;

x + x + x = 44 – 8 – 8;

3x = 28;

x = 28/3 = 9.3 cm;

AC = 9.33 cm;

AB = BC = 9.33 + 8 = 17.33 cm.

Answer: in the first case AB and BC are equal to 12 cm, AC is equal to 20 cm; in the second case AB and BC are equal to 17.33 cm, AC is equal to 9.33 cm.