Question 858986
As a rectangle is bounded by two pairs of equal sides a and b, the formula for its perimeter is:
{{{P = 2a + 2b}}}.
Or
{{{P = 2L + 2W}}}
If we are talking about length and width.


The length of a rectangle is 7 feet longer then twice the width.
{{{L = 2W + 7}}}


Now we can plug {{{2W + 7}}} in the place of L in the formula for perimeter and 86 for in the place of P.
{{{86 = 2(2W + 7) + 2W}}}
Expand the bracket and collect like terms:
{{{86 = 6W + 14}}}
{{{72 = 6W}}}
{{{W = 12}}}
The width of the rectangle is 12 feet.


Finding length:
{{{L = 2W + 7}}}
{{{L = 2*12 + 7 = 31}}}
Its length is 31 feet.

Now you want to check.
{{{P = 2L + 2W}}}
{{{86 = 2*31 + 2*12}}}
All good.