12. the square and rectangle shown below have the same perimeter length show that the length of the rectangle (3x + 1) centimetres

Lets call the perimeter P and the length of the rectangle l.  The first figure is a square with side length 2x + 2 so P = 4(2x + 2) = 8x + 8.  For the rectangle, P = 2l + 2(x + 3) = 2l + 2x + 6.  These values both equal P so they must equal each other.  8x + 8 = 2l + 2x + 6.  Now we have to solve for l.  

8x + 8 = 2l + 2x + 6  
8x + 2 = 2l + 2x
6x + 2 = 2l
3x + 1 = l