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"##