The perimeter of the triangle is 20cm. How long can the sides of a triangle be if it is isosceles and one of its sides is 8cm long?

The perimeter is the sum of the lengths of all sides of the shape. A triangle is called isosceles if the angles at the base are equal and the two sides are equal. There are two solutions to the problem.
First, let’s write down the perimeter for the case with an isosceles triangle:
P = a + a + b
P = a + b + b
Proceeding from this, either the length given in the problem has an equal side to it, or does not. Let’s consider each case separately:
1.a + a + 8 = 20
2a + 8 = 20
2a = 20-8
2a = 12
a = 6
Answer: 6, 6 and 8.
2.a + 8 + 8 = 20
a + 16 = 20
a = 20-16 = 4
Answer: 8, 8 and 4.