Question 115554
The length is 5 inches more than 2 times the width.  2 times the width is 2w, and 5 inches more than that is 2w + 5, so now we can say that:


{{{l=2w+5}}}


The perimeter of a rectangle is given by {{{P=2l+2w}}} and we know that the perimeter is 40 inches, so {{{2l+2w=40}}}.


Now substitute the expression we developed for l into the perimeter equation:


{{{2(2w+5)+2w=40}}}


Distribute
{{{4w+10+2w=40}}}


Collect like terms
{{{6w+10=40}}}


Add -10 to both sides
{{{6w=30}}}


Divide both sides by 6
{{{w=5}}}


Now we know the width is 5 inches, so put that into our expression for the length:
{{{l=2(5)+5=10+5=15}}}


And the length is 15 inches.


Check:
{{{2(15)+2(5)=30+10=40}}}, so those measurements give the correct perimeter.
{{{2(5)+5=10+5=15}}}, so the length and width have the correct relationship.  The answer checks.