Question 949266

first, you know that the window is a rectangular, and the area is {{{A=L*W}}}

given that the length {{{L}}} of a window is  {{{5ft}}}  more than its width {{{W}}},
so, we have {{{L=W+5ft}}}...eq.1

if the area of the window is {{{A=36ft^2}}}, then we have

{{{36ft^2=L*W}}}....substitute {{{L}}} from eq.1

{{{36ft^2=(W+5ft)*W}}}......solve for {{{W}}}

{{{36ft^2=W^2+5ft*W}}}

{{{0=W^2+5ft*W-36ft^2}}}

{{{0=W^2+5ft*W-36ft^2}}}...factor completely

{{{0=W^2+9ft*W-4ft*W-36ft^2}}}

{{{0=(W^2+9ft*W)-(4ft*W+36ft^2)}}}

{{{0=W(W+9ft)-4ft(W+9ft)}}}

{{{(W-4ft)(W+9ft) = 0}}}

solutions:

if {{{(W-4ft) = 0}}}=> {{{W=4ft}}}

if {{{(W+9ft) = 0}}}=>{{{W=-9ft}}}..we cannot use this solution, the width cannot be negative

so, the width is {{{highlight(W=4ft)}}}

go to eq.1 and find the length:

{{{L=W+5ft}}}...eq.1

{{{L=4ft+5ft}}}

{{{highlight(L=9ft)}}}