Question 722233
Let s, m and l represent the short, middle and long pieces, respectively
We have the following equations
s + m + l = 85 [sum of lengths]
l = 3s [longest three times as long as shortest]
l = m + 13 [longest is 13 cm longer than the middle piece]
Substitute l = 3s into the 1st and 3rd equation
s + m + 3s = 85
3s = m + 13 -> m = 3s - 13
s + (3s-13) + 3s = 85
7s = 98
s = 14
So l = 3s = 3*14 = 42
The longest piece is 42 cm