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.