Xavier wants to cover a floor measuring 110 cm by 90 cm with square tiles of the same size. Given that he uses only whole tiles, find
- the largest possible length of the side of each tile.
- the number of tiles that are needed to cover the floor.
(a)
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110
The highest common factor of 90 and 110 is 10.
Largest possible length of the side of each tile = 10 cm
(b)
Number of tiles arranged lengthwise
= 110 ÷ 10
= 11
Number of tiles arranged breadthwise
= 90 ÷ 10
= 9
Number of tiles to cover the floor
= 11 x 9
= 99
Answer(s): (a) 10 cm; (b) 99