Question 126609
The length of the original rectangle is L, and the width is W.  We also know that {{{L=W+7}}}.


If we decrease the length by 3 we get {{{L-3}}}, and if we increase the width by 2, we get {{{W+2}}}.


The perimeter of a rectangle is given by {{{P=2L+2W}}}, but we only know the perimeter of the new rectangle, so we have to use {{{P[n]=2(L-3)+2(W+2)=32}}}.   But while we're at it, let's substitute {{{W+7}}} for L so that we have a single equation in a single unknown.  {{{P[n]=2((W+7)-3)+2(W+2)=32}}}


Now collect terms and solve:
{{{2W+8+2W+4=32}}}
{{{4W+12=32}}}
{{{4W=20}}}
{{{W=5}}}


Since W is 5, L must be 5 + 7 = 12.


Check:
If we decrese the length by 3, we get 9, and if we increase the width by 2 we get 7.  (2 * 9) + (2 * 7) = 18 + 14 = 32.  Answer checks.