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”##