Nick wants to cover a floor measuring 120 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 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The highest common factor of 90 and 120 is 30.
Largest possible length of the side of each tile = 30 cm
(b)
Number of tiles arranged lengthwise
= 120 ÷ 30
= 4
Number of tiles arranged breadthwise
= 90 ÷ 30
= 3
Number of tiles to cover the floor
= 4 x 3
= 12
Answer(s): (a) 30 cm; (b) 12