a person cleared a rectangular plot of land and covered it with gravel. then he got 8 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.
To determine the perimeter of the person's new patio, we need to find the side lengths of the rectangular plot of land.
Given that the person covered the rectangular plot of land with gravel, we can establish that the area of the gravel is equal to the area of the patio.
To calculate the area of the patio, we sum the areas of the eight wooden squares.
Area of the patio = 2^2 + 5^2 + 7^2 + 9^2 + 16^2 + 25^2 + 33^2 + 36^2
Area of the patio = 4 + 25 + 49 + 81 + 256 + 625 + 1089 + 1296
Area of the patio = 4425
Now, let's find the dimensions of the rectangular plot. We need to find two side lengths whose product equals 4425.
The factors of 4425 are: 1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 375, 405, 675, 1125, 1215, 2025, 3375, and 4050.
Since we are dealing with a rectangular plot, we need to find two factors that result in a rectangle shape. By examining these factors, we find that 45 and 99 are compatible, as their product equals 4455. However, 4455 is slightly larger than the area of the patio, which is 4425.
Therefore, we need to search for factors slightly smaller than 4455. We find that 45 and 99 are close enough to serve as the side lengths of the rectangular plot.
Perimeter of the patio = 2 * (length + width) = 2 * (45 + 99) = 2 * 144 = 288.
Therefore, the perimeter of the person's new patio is 288.