Question 966210
{{{W}}}= width of the playground in feet.
{{{L}}}= length of the playground in feet.
{{{W*L=900}}}= area of the playground in square feet.
The problem states that the width is 1/4 of the length,
which in formula is {{{W=L/4}}} .
Since I do not like denominators, I change that into an equivalent equation:
{{{W=L/4}}} ---> {{{4W=L}}} .
Then, substituting into {{{W*L=900}}} , we get
{{{W*(4W)=900}}} ---> {{{4W^2=900}}} ---> {{{W^2=900/4}}} ---> {{{W^2=225}}} ---> {{{W=sqrt(225)}}} ---> {{{highlight(W=15)}}} .
(The other solution for the equation would be {{{W=-sqrt(225)=-15}}} , but we are looking for a length, which is a positive number, so {{{w=-15}}} is not a solution to the problem).
Then, substituting the value found into {{{L=4W}}} , we get
{{{L=4*15}}} ---> {{{highlight(L=60)}}} .
{{{highlight(Length=60 ft)}}} , {{{highlight(Width=15 ft)}}} .