a person cleared a rectangular plot of land and covered it with gravel. then he got 9 square wooden sections of side lengths: 2,5,7,9,16,25,28,33 and 36. by placing the squares on the gravel with no two overlaping, the person built a patio which exactly covered the graveled surface. determine the perimeter of the persons new patio.

To determine the perimeter of the person's new patio, we need to calculate the sum of all the sides of the wooden squares that were used.

Let's calculate the perimeter step by step:

1. First, let's list the given side lengths of the wooden squares:
2, 5, 7, 9, 16, 25, 28, 33, and 36.

2. Now, let's sort these side lengths in descending order:
36, 33, 28, 25, 16, 9, 7, 5, and 2.

3. Starting with the largest square (36), we'll place it on the gravel plot. Let's calculate its perimeter:
The perimeter of a square is given by 4 * side length.
So the perimeter of the square with side length 36 is 4 * 36 = 144 units.

4. Now, let's move to the next largest square (33) and place it on the gravel, making sure it doesn't overlap with the previously placed square. Calculate its perimeter and add it to the running total:
The perimeter of the square with side length 33 is 4 * 33 = 132 units.
So the total perimeter now is 144 units + 132 units = 276 units.

5. Repeat the process for the remaining squares, calculating their perimeters and adding them to the running total:
- Perimeter of the square with side length 28: 4 * 28 = 112 units.
Total perimeter now: 276 units + 112 units = 388 units.

- Perimeter of the square with side length 25: 4 * 25 = 100 units.
Total perimeter now: 388 units + 100 units = 488 units.

- Perimeter of the square with side length 16: 4 * 16 = 64 units.
Total perimeter now: 488 units + 64 units = 552 units.

- Perimeter of the square with side length 9: 4 * 9 = 36 units.
Total perimeter now: 552 units + 36 units = 588 units.

- Perimeter of the square with side length 7: 4 * 7 = 28 units.
Total perimeter now: 588 units + 28 units = 616 units.

- Perimeter of the square with side length 5: 4 * 5 = 20 units.
Total perimeter now: 616 units + 20 units = 636 units.

- Perimeter of the square with side length 2: 4 * 2 = 8 units.
Total perimeter now: 636 units + 8 units = 644 units.

6. The final total perimeter of the person's new patio is 644 units.

Therefore, the perimeter of the person's new patio is 644 units.