Question 119183
If the ratio of width to length is 3:4, then we can say that {{{w/l=3/4}}}.  Cross-multiplying gives {{{3l=4w}}} or {{{l=4w/3}}}.


The area of a rectangle is given by {{{A=lw}}}.  We know that the area is 108 square centimeters, so we can say:  {{{lw=108}}}.


Now we can substitute {{{4w/3}}} for {{{l}}}


{{{(4w/3)w=108}}} or {{{(4/3)w^2=108}}}


Multiply by 3/4:


{{{w^2=81}}}


{{{w=9}}}  (actually, w = plus or minus 9, but we can exclude the -9 result because we are looking for a positive number length measurement)


{{{l=(4/3)(9)=12}}}


So the width is 9 and the length is 12.