Length of the shortest side of a triangle

Question

A certain triangle has the longest side three times its shortest side. The middle side is five less than the longest side. The perimeter of the triangle is 37 cm. What is the length of the shortest side?

Answer 1

L=3S or S=L/3

M=L-5

L+M+S =37

L+L-5 + L/3 = 37

3L + 3L -15 + L = 111

7L = 111+15 = 126

L = 126/7 = 18 cm = length of the longest side

M=L-5 = 13 cm = length of the middle side

S= L/3 = 18/3 = 6 cm = length of the smallest side

18+13+6= 37 cm