Question 686852
Let the width = {{{ w }}}
The length is {{{ w + 5 }}}
let {{{ A }}} = area
{{{ A = w*( w + 5 ) }}}
{{{ 84 = w^2 + 5w }}}
{{{ w^2 + 5w - 84 = 0 }}}
use the quadratic formula
{{{ w = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 1 }}}
{{{ b = 5 }}}
{{{ c = -84 }}}
{{{ w = (-5 +- sqrt( 5^2 - 4*1*(-84) )) / (2*1) }}} 
{{{ w = (-5 +- sqrt( 25 + 336 )) / 2 }}} 
{{{ w = (-5 +- sqrt( 361 )) / 2 }}} 
{{{ w = (-5 +- 19) / 2 }}} ( ignore the negative square root )
{{{ w = ( -5 + 19 ) / 2 }}}
{{{ w = 14/2 }}}
{{{ w = 7 }}}
{{{ w + 5 = 12 }}}
The width is 7 in
The length is 12 in
check:
{{{ A = w*( w+5 ) }}}
{{{ 84 = 7*( 7 + 5 ) }}}
{{{ 84 = 84 }}}
OK