One side of a triangle is half the longest side. the third side is 8 feet less than the longer side. the perimeter is 47. find all three sides.

Let's call the longest side x.
One side of the triangle is x/2, or 0.5x
One side of the triangle is x - 8
And the third side would then be x

If we know the perimeter is 47, then we know that all of these sides add together to make 47, so we can solve for x:
0.5x + x + x - 8 = 47
2.5x - 8 = 47
+ 8
2.5x = 55
÷ 2.5
x = 22

So now that we know x, we can just substitute it in to the sides.
Side 1: 0.5 × 22 = 11
Side 2: 22 - 8 = 14
Side 3: And of course x is just 22

I hope this helps!