Question 120072
First we know that the area of a rectangle is given by {{{A=lw}}}, so we can write:


{{{lw=2700}}}


But we also know that the length, {{{l}}}, is three times the width {{{w}}}, so we can write:


{{{l=3w}}}


Now we can change the first equation to read:


{{{3w*w=2700}}}, or {{{3w^2=2700}}}


Divide both sides by 3


{{{w^2=900}}}


Take the square root of both sides:


{{{sqrt(w^2)=sqrt(900)}}}


{{{w=30}}} or {{{w=-30}}}.  However, since we are looking for a measure of length, we can exclude the {{{w=-30}}} result.


Since we know that {{{l=3w}}}, we now know that {{{l=3*30=90}}}.


So the dimensions of the playground are 90 feet by 30 feet.


Check:

{{{90*30=2700}}} and {{{3*30=90}}}:  Checks!


Hope that helps.
John