Mathematics
A rectangular 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 and the edges of the floor, what fraction of the floor is uncovered?
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Answer
Let ABCD be the rectangular floor and PQRS be the carpet.
Area of floor = l × b = 15 × 8 = 120 m2 = 120 × (100 cm)2 = 1200000 cm2
Area of a tile = 50 cm × 25 cm = 1250 cm2
No. of required tiles =
Substituting the values we get,
No. of required tiles = = 960.
From figure,
Length of carpet (PQ) = 15 – 1 – 1
= 15 – 2
= 13 m
Breadth of carpet (QR) = 8 – 1 – 1
= 8 – 2
= 6 m
Area of carpet = l × b
= 13 × 6
= 78 m2.
Area of floor which is uncovered by carpet = Area of floor – Area of carpet
= 120 – 78
= 42 m2
Fraction of floor uncovered =
= .
Hence, number of tiles required to cover the floor = 960 tiles and is the fraction of floor uncovered.
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