My actual question is this " The length of the base of an isosceles triangle is one third the length of one of its legs. If the perimeter of the triangle is 71 inches, what is the length of the base?"

Perimeter is the sum of all the sides.

Hence, base + leg + leg = 71 in

You are told that the base is a third of a leg, hence,

3base = leg

Put that into your initial equation and solve for the base.