Question 677301
2*(l+w) = 54
or, l+w = 54/2 = 27
or, l = 27 - w
Now, lw=72
By substituting l, (27-w)*w = 72
{{{27w - w^2 = 72}}}
{{{0 = 72 - 27w + w^2}}}
{{{w^2 - 27w + 72 = 0}}}
By middle term factor,
{{{w^2 - 24w - 3w + 72 = 0}}}
{{{w*(w-24) - 3(w-24) = 0}}}
{{{(w-24)*(w-3)=0}}}
Either, w-24=0 => w=24
OR, w-3=0 => w=3
If w=24, l = 27-24 = 3
If w=3, l = 27-3 = 24
Therefore length = 24 ft and width = 3 ft