Question 607174

you are given:

The width {{{W}}} of a rectangle is {{{6 km}}} less than twice its length {{{L}}}}

means: {{{W=2L-6km}}}

you know that the area of a rectangle is {{{A=L*W}}}

and, you also know that the area is {{{80km^2}}}

so, use
 
{{{A=L*W}}}...plug in all known values

{{{80km^2=L*(2L-6km)}}}

{{{80km^2=2L^2-6Lkm)}}}..move {{{80km^2}}} to the right and you will have quadratic equation to solve for {{{L}}}

{{{0=2L^2-6Lkm-80km^2)}}}....use quadratic formula

{{{L = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}....{{{a=2}}}, {{{b=-6km}}} and {{{c=-80km^2}}}


{{{L = (-(-6km) +- sqrt( (-6km)^2-4*2*(-80km^2) ))/(2*2) }}}

{{{L = (6km +- sqrt(36km^2+640km^2 ))/4 }}}

{{{L = (6km +- sqrt(676km^2 ))/4 }}}

{{{L = (6km +- (26km ))/4 }}}....disregard negative value because the length cannot be negative

{{{L = (6km + 26km )/4 }}}

{{{L = 32km /4 }}}

{{{L = 8km }}}......now we can find the {{{W}}}

{{{W=2L-6km}}}...plug in {{{L}}}

{{{W=2*8km-6km}}}

{{{W=16km-6km}}}

{{{W=10km}}}


check:


{{{A=L*W}}}

{{{A=8km*10km}}}

{{{A=80km^2}}}