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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Question

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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KnowledgeBoat · Accepted 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.

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?

Mensuration

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Mensuration

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