Question 250256
Let width = w
Therefore lengh = 15 - w
Area = width*length
     {{{= w(15-w)}}}
     {{{= 15w - w^2}}}
It is given that area = 54

=> {{{54 = 15w - w^2}}}
=> {{{w^2 - 15w + 54 = 0}}}
=> {{{w^2 - 6w - 9w + 54 = 0}}}
=> {{{w(w-6) -9(w-6) = 0}}}
=> {{{(w-6)(w-9)=0}}}
=> w = 6 or w = 9
Therefore width is 6 and the length is 9