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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”##