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

Feb 9, 2015

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
$P = 2 \cdot \left(L + W\right)$
So we have
$2 \cdot \left(L + W\right) = 300$
or $L + W = 150$

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

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

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