let

l = the length of the field

w = the width of the field

P = 1040 ft the perimeter of the field

The football field is rectangular in shape thus its perimeter is:

P = 2(l + w)

2(l + w) = 1040 divide both sides by 2

l + w = 520

The length of the field is 120 feet less than 3 times the width:

l = 3w - 120

by solving the system of equations

l + w = 520

l = 3w - 120

we find

l = 360 ft

w = 160 ft

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

the dimensions if the field are: the length is 360 feet; the width is 160 feet.