Michael wants to cover a floor measuring 300 cm by 140 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 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The highest common factor of 140 and 300 is 20.
Largest possible length of the side of each tile = 20 cm
(b)
Number of tiles arranged lengthwise
= 300 ÷ 20
= 15
Number of tiles arranged breadthwise
= 140 ÷ 20
= 7
Number of tiles to cover the floor
= 15 x 7
= 105
Answer(s): (a) 20 cm; (b) 105
