The length of pool is: 30 feet
and the width of pool is: 18 feet
Let the length of the swimming pool be denoted by: l
and the width of the swimming pool be denoted by: w
The area of the swimming pool will be:
[tex]Area=l\times w[/tex]
Here it is given that:
The width of the swimming pool is 12 feet less than the pools length.
i.e.
[tex]w=l-12----------(1)[/tex]
and the area of pool is: 540 square feet.
i.e.
[tex]l\times w=540\\\\i.e.\\\\l(l-12)=540\\\\i.e.\\\\l^2-12l-540=0[/tex]
i.e.
[tex]l^2-30l+18l-540=0\\\\i.e.\\\\l(l-30)+18(l-30)=0\\\\i.e.\\\\(l+18)(l-30)=0\\\\i.e.\\\\l=-18\ and\ l=30[/tex]
but l can't be negative, since the length of something can't be negative.
Hence, we get:
[tex]l=30[/tex]
and on putting the value of l in equation (1) we get:
[tex]w=30-12\\\\i.e.\\\\w=18[/tex]
