1. To calculate the amount of fencing needed for the swimming pool, we can use the formula for the perimeter of a rectangle. The perimeter of a rectangle is given by the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the length of the pool is 36 ft. and the width is 20 ft. We need to add 9 ft. on each side for the fence, so we'll increase the length and width accordingly.
New length = 36 ft. + 9 ft. + 9 ft. = 54 ft.
New width = 20 ft. + 9 ft. + 9 ft. = 38 ft.
Now we can calculate the perimeter:
P = 2(54 ft. + 38 ft.)
P = 2(92 ft.)
P = 184 ft.
Therefore, 184 ft. of fencing is needed to build the fence around the swimming pool.
2. To calculate the number of 4-in. by 4-in. tiles needed to cover the floor of the shower stall, we need to find the area of the shower floor and divide it by the area of one tile.
The area of the shower floor is given by the formula: A = length × width.
In this case, the length and width of the shower floor are both 36 inches.
A = 36 in. × 36 in.
A = 1296 sq. in.
The area of one tile is given by the formula: A_tile = length_tile × width_tile.
In this case, the length and width of one tile are both 4 inches.
A_tile = 4 in. × 4 in.
A_tile = 16 sq. in.
Now, we can calculate the number of tiles needed by dividing the area of the shower floor by the area of one tile:
Number of tiles = A / A_tile
Number of tiles = 1296 sq. in. / 16 sq. in.
Number of tiles = 81 tiles.
Therefore, 81 tiles are needed to cover the floor of the shower stall.