Question

# The ratio of the length (including the endzone) to the width of an NFL football field is 2.25. If the perimeter of the football field is 1040 feet, what are the dimensions of the field?

Performing transformations
The ratio of the length (including the endzone) to the width of an NFL football field is 2.25. If the perimeter of the football field is 1040 feet, what are the dimensions of the field?

2020-10-27
Let l be the length and w be the width so that the perimeter is: P=2l+2w
We find an expression for l in terms of w using the given perimeter: 1040=2l+2w
Divide both sides by 2: 520=l+w
520-w=l
The ratio of the length to the width is 2.25: l/w=2.25
$$\displaystyle\frac{{{520}-{w}}}{{w}}={2.25}$$
Multiply both sides by 2.25: 520-w=2.25w
Add w to both sides: 520=3.25w
Divide both sides by 3.25: 160=w
Solve for l using (1): l=520-160
l=360
So, the dimentions of the field are 360 feet by 160 feet