what is the least number of tiles that are needed to completely cover a rectangular center piece 3 yards by 5 yards if a rectangular decorative tile is 2 inches by 3 inches respectively?
3x5 yards = 108x180 inches
108x180 over 2x3 = 54x60 = 3240 tiles
hi steve why is it the answer is 1440 tiles i am confused how is it derived?
To solve this problem, we need to find the area of the rectangular center piece and the area of the decorative tile. Then we can determine how many tiles are needed to cover the rectangular center piece.
Step 1: Convert yards to inches.
Since the decorative tile is measured in inches, we should convert the dimensions of the rectangular center piece from yards to inches.
3 yards = 36 inches (1 yard = 36 inches)
5 yards = 60 inches
Step 2: Find the area of the rectangular center piece.
The area of a rectangle is calculated by multiplying its length by its width.
Area = Length x Width
Area = 36 inches x 60 inches
Area = 2160 square inches
Step 3: Find the area of the decorative tile.
The area of the decorative tile is calculated by multiplying its length by its width.
Area = Length x Width
Area = 2 inches x 3 inches
Area = 6 square inches
Step 4: Determine the number of tiles needed.
To determine the number of tiles needed, divide the area of the rectangular center piece by the area of the decorative tile.
Number of tiles = Area of rectangular center piece / Area of decorative tile
Number of tiles = 2160 square inches / 6 square inches
Number of tiles = 360 tiles
Therefore, the least number of tiles needed to completely cover the rectangular center piece is 360 tiles.