Question 1010081

{{{W=(-2x + 1)}}} feet
{{{L= (-3x +4)}}} feet, 
{{{A=450}}} square feet

{{{A=L*W}}}

{{{450=(-3x +4)*(-2x + 1)}}}

{{{450=(-3x)(-2x) + (-3x)1+4(-2x)+4*1)}}}

{{{450=6x^2 -3x-8x+4}}}

{{{450=6x^2-11x+4}}}

{{{0=6x^2-11x+4-450}}}

{{{0=6x^2-11x-446}}}...use quadratic formula


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


{{{x = (-(-11) +- sqrt( (-11)^2-4*6*(-446) ))/(2*6) }}}

{{{x = (11 +- sqrt( 121+10704 ))/12 }}}

{{{x = (11 +- sqrt( 10825 ))/12 }}}

{{{x = (11 +- 104.04)/12 }}}

we will need only negative solution since in given length and width coefficient of {{{x}}} is negative number:

{{{x = (11 - 104.04)/12 }}}

{{{x =  -93.04/12 }}}

{{{x =  -7.753333333333333}}}..round it

{{{highlight(x =  -7.75) }}}

now find the length and the width

{{{W=-2*(-7.75) + 1}}} feet=>{{{W=15.5 + 1}}}feet =>{{{highlight(W=16.5 )}}}
{{{L= -3(-7.75) +4}}} feet =>{{{L= 23.25 +4}}} feet=>{{{highlight(L= 27.25 )}}} feet


check the area:

{{{27.25*16.5=449.625}}} rounded to {{{450}}}