Question 752687
given:

area is {{{A=216cm^2}}} and 

perimeter is {{{P=60cm}}}

if the length is {{{L}}} and the width is {{{W}}}, then

{{{L*W=216cm^2}}}......eq.1 and

{{{2(L+W)=60cm}}}.....eq.2
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start with {{{2(L+W)=60cm}}}.....eq.2 and solve for {{{L}}}

{{{L+W=60cm/2}}}

{{{L+W=30cm}}}

{{{L=30cm-W}}}.....plug it in eq. 1 and solve for {{{W}}}

{{{(30cm-W)b=216cm^2}}}......eq.1

{{{30*Wcm-W^2=216cm^2}}}

{{{0=W^2-30*Wcm+216cm^2}}} or

{{{W^2-30*Wcm+216cm^2=0}}} ....use quadratic formula


{{{W = (-(-30) +- sqrt( (-30)^2-4*1*216 ))/(2*1) }}}


{{{W = (30 +- sqrt(900-864 ))/2 }}}


{{{W = (30 +- sqrt(36 ))/2 }}}

{{{W = (30 +- 6 )/2 }}}

solutions;

{{{W = (30 +6 )/2 }}}

{{{W = 36/2 }}}

{{{W = 18cm }}}

or

{{{W = (30 -6 )/2 }}}

{{{W = 24/2 }}}

{{{W = 12cm }}}


now find {{{L}}}

{{{L=30cm-W}}}

if {{{W = 18 cm}}} => {{{L=30cm-18cm}}}  => {{{L=12cm}}}

if {{{W = 12cm }}} => {{{L=30cm-12cm}}}  => {{{L=18cm}}}

since the length is usually greater we will say that {{{L=18cm}}} and {{{W = 12cm }}}