Luke wants to cover a floor measuring 280 cm by 120 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 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 280: 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The highest common factor of 120 and 280 is 40.
Largest possible length of the side of each tile = 40 cm
(b)
Number of tiles arranged lengthwise
= 280 ÷ 40
= 7
Number of tiles arranged breadthwise
= 120 ÷ 40
= 3
Number of tiles to cover the floor
= 7 x 3
= 21
Answer(s): (a) 40 cm; (b) 21