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Question
A rectangular floor 45 in long and 12 m broad is to be paved exactly with square tiles, of side 60 cm. Find the total number of tiles required to pave it.
If a carpet is laid on the floor such as a space of 50 cm exists between its edges and the edges of the floor, find what fraction of the floor is uncovered.
Solution
Length of a rectangular floor = 45m
Breadth of a rectangular floor = 12m
∴ Area of a rectangular floor
= 45m x 12m
= 540m2
Side of a square title
= 60cm
= 0.6m
∴ Area of one square title
= (0.6m)2
= 0.36m2
Thus, total number of titles required
= `"Area of a rectangular floor"/"Area of one square title"`
= `(540)/(0.36)`
= 1500
Space
= 50cm
= 0.5m
⇒ On both sides, space
= 0.5 x 2
= 1m
∴ Area of carpet
= (45 - 1) x (12 - 1)
= 44 x 11
= 484m2
⇒ Uncovered area
= Area of a rectangular floor - Area of carpet
= (540 - 484)m2
= 56m2
∴ Fraction of floor uncovered
= `"Uncovered area"/"Area of a rectangular floor"`
= `(56)/(540)`
= `(14)/(135)`.
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