a person cleared a rectangular plot of land and covered it with gravel. then he got 9 square wooden sections of side lengths: 2,5,7,9,16,25,33 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.

Question

a person cleared a rectangular plot of land and covered it with gravel. then he got 9 square wooden sections of side lengths: 2,5,7,9,16,25,33 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.

Answer 1

To determine the perimeter of the person's new patio, we need to find the dimensions of the rectangular plot of land. Once we have the dimensions, we can calculate the perimeter.

Let's start by arranging the squares on the rectangular plot. As mentioned, there are 9 wooden squares with side lengths of 2, 5, 7, 9, 16, 25, 33, and 36.

Since we want to cover the rectangular plot completely with no overlap, we can arrange the squares in descending order from the largest to the smallest. Here's one possible arrangement:

1. Start by placing the largest square, which has a side length of 36, in one corner of the rectangular plot.
2. Place the next largest square, with a side length of 33, adjacent to the previous square.
3. Continue this process, placing each square adjacent to the previous one until you have used all of the squares.

After arranging the squares, you will notice that they form a rectangle, and the dimensions of this rectangle determine the dimensions of the patio.

Let's calculate the dimensions:

Starting with the longest side, we have a side length of 36. The next longest side, which is adjacent to it, will be the sum of the side lengths of the remaining squares:

36 + 33 + 25 + 16 + 9 + 7 + 5 + 2 = 133

This means the longer side of the rectangle is 133. To find the shorter side, we need to remove the length of the largest square (36):

133 - 36 = 97

So, the dimensions of the rectangular plot, and therefore the patio, are 133 by 97.

Finally, we can calculate the perimeter of the patio by adding the lengths of all four sides:

Perimeter = 2 * (length + width)
Perimeter = 2 * (133 + 97)
Perimeter = 2 * 230
Perimeter = 460 units

Therefore, the perimeter of the person's new patio is 460 units.