11. The area of a rectangle remains unchanged when either its length is increased by 6 units and width decreased by 2 units, or its length decreased by 12 units and its width increased by 6 units. If the perimeter of the original rectangle is $x$ units, find the value of $x$.
11. Answer: 132
Let the length and width of the original rectangle be $L$ and $W$ respectively. Then
$$
L W=(L+6)(W-2) \text { and } L W=(L-12)(W+6) .
$$

Simplifying the above equations, we obtain
$$
L-2 W=12 \text { and } 3 W-L=6 .
$$

Solving the simultaneous equations, we get $L=48$ and $W=18$. Hence the perimeter of the rectangle is 132 units.