Question

the third side of an isosceles triangle is 8 inches shorter than the other two sides the perimeter of the triangle is 70 inches find the length of each side

Answer 1

Isosceles triangle has 2 sides that are the same length. So what you have is three sides that measure: x, x, and (x-8). 70 = x + x + (x-8).
70 = x + x + x - 8
78 = 3x
x = 26.
and 26 - 8 = 18.
So two of your sides are 26 inches and the last side is 18 inches. 

Answer 2

If we add 8 inches to the third side, then the triangle will be equilateral, and the perimeter will be 70+8=78 inches.

The sides of a 78-inch equilateral triangle is 78/3=26 inches.

So the equal sides of the isosceles triangle are both 26 inches, while
the third side is 26-8=18 inches.

Check: 18+26+26=70 inches   ✔