let

x = the length of the first side

y = the length of the second side

z = the length of the third side

the perimeter of a triangle is 60 feet:

x + y + z = 60

the third side is four times the length of the second side

z = 4y

the first side is 6 feet less than the second side

x = y - 6

by solving the system of equations:

x + y + z = 60

z = 4y

x = y - 6

we find:

x = 5 ft

y = 11 ft

z = 44 ft

click here to see the step by step solution of the system of equations:

the length of the sides is: 5 ft, 11 ft and 44 ft.