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Question
A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. it is to be paved with square tiles of the same size. Find the least possible number of such tiles.
Solution
GIVEN: A rectangular yard is 18 m 72 cm long and 13 m 20 cm broad. It is to be paved with square tiles of the same size.
TO FIND: Least possible number of such tiles.
Length of the yard = 18 m 72 cm = 1800 cm + 72 cm = 1872 cm ...(∵ 1 m = 100 cm)
Breadth of the yard =13 m 20 cm = 1300 cm + 20 cm = 1320 cm
The size of the square tile of same size needed to the pave the rectangular yard is equal the HCF of the length and breadth of the rectangular yard.
Prime factorisation of 1872 = \[2^4 \times 3^2 \times 13\]
Prime factorisation of 1320 = \[2^4 \times 3^2 \times 13\]
HCF of 1872 and 1320 = \[2^3 \times 3 = 24\]
∴ Length of side of the square tile = 24 cm
Number of tiles required =
`"Area of the courtyard"/"Area of each tile"= "length xx Breadth"/"(Side)"^2 =(1872 "cm" xx 1320 "cm")/((24 "cm")^2)` = 4290
Thus, the least possible number of tiles required is 4290.
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