Question

If a storm window is 315 square inches, what are the dimensions if the window is 6 inches higher than it is wide

Answer 1

$\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=\stackrel{\textit{6 more than \underline{w}}}{w+6}\\ A=315 \end{cases}\implies 315=(w+6)(w) \\\\\\ 315=w^2+6w\implies 0=w^2+6w-315 \\\\\\ (w+21)(w-15)=0\implies w= \begin{cases} -21\\ \boxed{15} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill w=15\qquad \stackrel{w+6}{L=21}~\hfill$