Question 129949
Let L=length, w=width


Since "its length is 2 meters more than twice its width", this means 


{{{L=2w+2}}}



Remember the formula for the perimeter of a rectangle is 


{{{P=2w+2L}}}



{{{16=2w+2(2w+2)}}} Plug in {{{P=16}}} and {{{L=2w+2}}}




{{{16=2w+4w+4}}} Distribute



{{{16=6w+4}}} Combine like terms on the right side



{{{0=6w+4-16}}}Subtract 16 from both sides



{{{-6w=4-16}}} Subtract 6w from both sides



{{{-6w=-12}}} Combine like terms on the right side



{{{w=(-12)/(-6)}}} Divide both sides by -6 to isolate w




{{{w=2}}} Divide


So the width is 2 m 




{{{L=2(2)+2}}} Now plug in {{{w=2}}}



{{{L=4+2}}} Multiply



{{{L=6}}}  Add



So the length is 6 m