Question

What are the dimensions of a soccer field if the perimeter is 300 years and the length is 50 yards longer than the width?

Answer 1

width = 50 and length = 100

For simplicity, we will use the letters W for width, L for length and P for perimeter.

For a rectangular field
`P = 2 * (L + W)`
So we have
`2 * (L + W) = 300`
or `L + W = 150`

We are told that
`L = W + 50`
So `L + W = 150` can be re-written as `(W+50) + W = 150`
which can be simplified:
`2W + 50 = 150`
`2W = 100`
`W = 50`

And since `L = W +50`
`L = 50 + 50 = 100`

Therefore the width is 50 (yards) and the length is 100 (yards).