Since the longest and middle pieces are explained in terms of the shortest piece, lets call the shortest piece x.

Since the longest is 4 times the shortest, then the longest = 4x.

Since the middle is 2 feet longer, the the middle = x+ 2.

Now since all pieces add up to 20...make an equation.

4x + (x + 2) + x = 20

6x = 18

x = 3.

Now plug in x and you'll have all the lengths.