Let's begin by listing out the given information:
This is a rectangle. It has a length & width
The total area of the rectangle is 72 square feet
Its length is 15 more than 3 times its width
Mathematically,
[tex]\begin{gathered} Length=15+3\cdot w \\ Length=15+3w \end{gathered}[/tex]Now, the area of a rectangle is given by the product of the length & width
[tex]\begin{gathered} Area=length\times width \\ Area=72 \\ length=15+3w \\ width=w \\ \Rightarrow72=(15+3w)\times w \\ 72=15w+3w^2 \\ \text{Rearranging the equation, we have:} \\ 3w^2+15w-72=0 \end{gathered}[/tex]