Question 682982


The length {{{L}}} of a rectangular storage room is {{{8ft}}} longer than its width {{{W}}}.   

{{{L=W+8ft}}}............eq. 1

if the area {{{A=L*W}}} of the room is {{{105ft^2}}}, than


{{{105ft^2=L*W}}}.........eq. 2....substitute {{{L}}} from eq. 1


{{{105ft^2=(W+8ft)*W}}}....solve for {{{W}}}


{{{105ft^2=W^2+8Wft}}}


{{{W^2+8Wft-105ft^2=0}}}


{{{W = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


{{{W = (-8ft +- sqrt( (8ft)^2-4*1*(-105ft^2) ))/(2*1) }}}


{{{W = (-8ft +- sqrt(64ft^2+420ft^2) ))/2 }}}


{{{W = (-8ft +- sqrt(484ft^2) ))/2 }}}


{{{W = (-8ft +- 22ft )/2 }}}

find only positive root because the width cannot be negative

{{{W = (-8ft + 22ft )/2 }}}

{{{W = 14ft /2 }}}


{{{highlight(W = 7ft) }}}


now find the length {{{L}}}

{{{L=W+8ft}}}

{{{L=7ft+8ft}}}

{{{highlight(L=15ft)}}}