A floor which measures 15 m*8 m is to be laid with tiles measuring 50 cm*25 cm. Find the number of tiles required. Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges of the floor, what fraction of the floor is uncovered?
A floor which measures 15 m*8 m is to be laid with tiles measuring 50 cm*2
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50 cm = 0.5m and 25 cm = 0.25m
15m/0.5m = 30 tiles along the length of the room (15m)
8m/0.25m = 32 tiles along the width of the room (8m)
You will need 30*32 = 960 tiles
To leave 1 m between the carpet and wall on all sides, the carpet needs to be 2 m shorter in each dimension: (15-2)m by (8-2)m, or 13 by 6 meters. The carpet's area is 13*6 = 78 m2. The room's area is 15*8 = 120 m2. The fraction of the area uncovered is:
(120-78)/120 = 42/120 = 7/20