Japheth wants to cover a floor measuring 220 cm by 180 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 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
The highest common factor of 180 and 220 is 20.
Largest possible length of the side of each tile = 20 cm
(b)
Number of tiles arranged lengthwise
= 220 ÷ 20
= 11
Number of tiles arranged breadthwise
= 180 ÷ 20
= 9
Number of tiles to cover the floor
= 11 x 9
= 99
Answer(s): (a) 20 cm; (b) 99
