Question 731877

The length of a rectangle {{{L}}} is six times its width {{{W}}}:

{{{L=6W}}}......eq. 1
 
If the area {{{A=L*W}}} of the rectangle is {{{486cm^2}}} , find its perimeter {{{P}}}

start with
{{{A=L*W}}}...plug in given value for area

{{{486cm^2=L*W}}}...substitute {{{L}}} from eq. 1

{{{486cm^2=6W*W}}}......solve for {{{W}}}

{{{486cm^2=6W^2}}}

{{{486cm^2/6=W^2}}}

{{{81cm^2=W^2}}}

{{{W=sqrt(81cm^2)}}}

{{{highlight(W=9cm)}}}

now go back to eq. 1 and find {{{L}}}

{{{L=6W}}}......eq. 1

{{{L=6*9cm}}}

{{{highlight(L=54cm)}}}


now we can find  perimeter {{{P}}}

{{{P=2L+2W}}}

{{{P=2*54cm+2*9cm}}}

{{{P=108cm+18cm}}}

{{{highlight(P=126cm)}}}