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

1 Answer
Alan P.
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 * (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).

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