Answer:
A- The side length of the largest square tile Hector can use to tile his shed floor so that there are no gaps or overlaps is 48 inches
B- The number of square tiles Hector will need is 15 tiles
Explanation:
A- The given parameters are;
The size of the tiles cut by the company he found = 60 inches × 60 inches
The length of his shed floor = 240 inches
The width of his shed floor = 144 inches
The side length of the largest square tile is given as the highest common factor, HCF of 240 and 144 given as follows;
144/240 = 3/5
Therefore, we have the highest common factor of 144 and 240 = 144/3 = 48
Therefore, the side length of the largest square tile Hector can use to tile his shed floor so that there are no gaps or overlaps = 48 inches
B- The area of his shed floor = 240 inches × 144 inches = 34560 in.²
The area of one square tile = 48 inches × 48 inches = 2,304 in.²
The number of square tiles, n, Hector will need is given as follows;
The number of square tiles Hector will need = (The area of his shed floor)/(The area of one square tile)
The number of square tiles Hector will need = n =34560 in.²/(2,304 in.²) = 15
The number of square tiles Hector will need = 15 tiles.