Find the sides of an isosceles triangle if its perimeter is 78, and the side is 12 cm less than the base.

An isosceles triangle is a triangle in which the sides are equal:
AB = BC.
The perimeter of a triangle is the sum of all its sides:
P = AB + BC + AC.
Since the perimeter of this triangle is 78 cm, and the sides are 12 cm less than the base, we express:
x is the length of the sides AB and BC;
x + 12 – the length of the base of the speaker;
x + x + x + 12 = 78;
x + x + x = 78 – 12;
3x = 66;
x = 66/3 = 22;
AB = BC = 22 cm;
AC = 22 + 12 = 34 cm.
Answer: the base of the AC is 34 cm, the sides AB and BC are 22 cm.