# The perimeter of a football field rink is 346 yards. If the length is 14 yards more than 2 times the width, what are the dimensions?

##l=120″yds”## ##w=53″yds”##

A football field resembles as a rectangle.

The perimeter of a rectangle can be determined by the equation:

##P=2l+2w rarr## equation 1

where: ##P rArr##perimeter ##l rArr##length ##w rArr## width

Converting the given to an algebraic expression gives us:

##color(red)l=14″yds”+2w rarr##equation 2

Using this expression, we can replace ##color(red)l## from equation 1 and come up with a formula that would determine the value of the width.

From equation 1, we have:

##P=2color(red)l+2w##

##P=2(color(red)(14″yds”+2w))+2w##

##rarr##simplifing the equation gives us,

##color(blue)P=28″yds”+6w##

then,

##color(blue)(346″yds”)=28″yds”+6w##

##6w=346″yds”-28″yds”##

##6w=318″yds”##

##w=(318″yds”)/6##

##w=53″yds”##

Then, to find the length, simply substitute the value of the width to the equation 2.

##l=14″yds”+2w##

##l=14″yds”+2(53″yds”)##

##l=120″yds”##

##:.## the dimension of the field is ##120″yds”## by ##53″yds”##