jmc

We can look at the region as a rectangle with a smaller staircase-shaped region removed from its upper-right corner. We extend two of its sides to complete the rectangle: Dissecting the small staircase, we see it consists of ten 1 ft by 1 ft squares and thus has area 10 square feet. Let the height of the rectangle have length $x$ feet, so the area of the rectangle is $9x$ square feet. Thus we can write the area of the staircase-shaped region as $9x-10$. Setting this equal to $53$ and solving for $x$ yields $9x-10=53\Rightarrow x=7$ feet.

Finally, the perimeter of the region is $7+9+3+5+8\cdot 1=\boxed{32}$ feet. (Notice how this is equal to the perimeter of the rectangle -- if we shift each horizontal side with length 1 upwards and each vertical side with length 1 rightwards, we get a rectangle.)