Key to "The ratio of the length (including the endzone)..."

High School
Geometry
High school geometry
Performing transformations

Cheyanne Leigh

Answered question

2020-10-26

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?

Answer & Explanation

Macsen Nixon

Skilled2020-10-27Added 117 answers

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

\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

Jeffrey Jordon

Expert2021-10-13Added 2605 answers

Answer is given below (on video)

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