Question 125152
The side of the square is s.


The length of the rectangle is then 2s, so {{{l=2s}}}, and


The width of the rectangle is s - 1, so {{{w=s-1}}}



The perimeter of a rectangle is given by {{{P[r]=2l+2w}}} and the perimeter of a square is given by {{{P[s]=4s}}}.


Substituting in the expression for {{{P[r]}}}, we get {{{P[r]=2(2s)+2(s-1)}}}


But {{{P[r]=P[s]+3}}}, so


{{{2(2s)+2(s-1)=4s+3}}}
{{{4s+2s-2=4s+3}}}


{{{cartoon(4s+2s-2=4s+3,cross(4s)+2s-2=cross(4s)+3,2s-2=3)}}}


{{{2s=5}}}
{{{s=5/2}}}

Side of the square is {{{5/2}}}.  Length of the rectangle is {{{2*(5/2)=5}}},  Width of the rectangle is {{{(5/2)-1=3/2}}}


Check answer


{{{P[r]=2(5)+2(3/2)=10+3=13}}}


{{{P[s]=4(5/2)=20/2=10}}}


And finally, {{{10 + 3=13}}}