How do you find the sides of a isosceles triangle in a algebraic equation when given the perimeter?

In every isosceles triangle you have a base and two equal sides .

So, the perimeter is the sum of the sides:

Solving for the sides, you have

So, you take the perimeter, subtract the base, and you have the sum of the two other sides. Divide that result by 2, and you have the length of one of the sides.

Note that if you only know the perimeter (i.e. if you don't know the length of the base), you can't deduce the length of the sides.