Question 971585
On a rectangle, 

if the length {{{L}}} is {{{5}}} less than {{{3}}} times the width {{{W}}}, then

{{{L=3W-5}}}....eq.1


and if the area  {{{A=L*W}}}is {{{112cm^2}}}, then

{{{L*W=112}}}....eq.2............substitute {{{L}}} from eq.1

{{{(3W-5)*W=112}}}......solve for {{{W}}}

{{{3W^2-5W=112}}}....factor...write {{{-5W}}} as {{{-21W+16W}}}

{{{3W^2-21W+16W-112=0}}}......group

{{{(3W^2-21W)+(16W-112)=0}}}

{{{3W(W-7)+16(W-7)=0}}}

{{{(3W+16)(W-7)=0}}}

solutions: since we have a rectangle, we will need only positive solution and that is {{{ (W-7)=0}}}=>{{{highlight(W=7cm)}}}

now go to eq.1 and solve for {{{L}}}


{{{L=3*7-5}}}....eq.1

{{{L=21-5}}}

{{{highlight(L=16cm)}}}