Seth wants to cover a floor measuring 280 cm by 200 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 200: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
Factors of 280: 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The highest common factor of 200 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
= 200 ÷ 40
= 5
Number of tiles to cover the floor
= 7 x 5
= 35
Answer(s): (a) 40 cm; (b) 35