Question 104718
Perimeter of a rectangle is equal to the sum of its four sides.
A rectangle has two sides that represent its length and
two sides that represent its width. So 
perimeter = 2 times length plus 2 times width
P = 2L + 2W
Now for this rectangle we are told that the
length = 2 times width minus 1
L = 2W - 1
We are also told that the 
width = 1/7 perimeter plus 3
W = 1/7(P) + 3
W = P/7 + 3
Ok lets go back to the original equation for perimeter
P = 2L + 2W
since we have shown that L = 2W - 1 we can substitute 2W - 1 for L in
P = 2L + 2W
P = 2(2W-1) + 2W
Now if we use this equation with W = P/7 +3 we have a system of equations in two varibles that we can solve for.
So here are the two equations we will be working with:
P = 2(2W-1) + 2W
AND
W = P/7 + 3
Lets solve the system of equations using the substitution method.
Since W = P/7 + 3 we can substitute P/7 + 3 for the W in 
P = 2(2W-1) + 2W
P = 2(2(P/7 + 3)-1) + 2(P/7 + 3)
Now we have and equation with just one variable to solve for
P = 2(2(P/7 + 3)-1) + 2(P/7 + 3)
P = 2(2P/7 + 6 - 1) + 2P/7 + 6
P = 4P/7 + 12 - 2 + 2P/7 + 6
P = 6P/7 + 16
P = 6P/7 + 112/7
{{{P = (6P+112)/7}}}
7P = 6P + 112
P = 112
<B>The perimeter is 112</B>
use this to find the width
W = P/7 + 3
W = 112/7 + 3
W = 16 + 3
W = 19
<B>The width of the rectangle is 19</B>
use this to find the length
L = 2W - 1
L = 2(19) - 1
L = 38 - 1
L = 37
<B>The length of the rectangle is 37</B>
check answers with formula for perimeter
P = 2L + 2W
112 = 2(37) + 2(19)
112 = 74 + 38
112 = 112