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.
✓
Answer
Length of the yard $= 18m 72cm = 1800cm + 72cm = 1872cm$
Breadth of the yard $= 13m 20cm = 1300cm + 20cm = 1320cm$
Area of the yard $= 1872 \times 1320 = 2471040$
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 length and breadth
$1872 = 2^4 \times 3^2 \times 13$
$1320 = 2^3 \times 3 \times 5 \times 11$
HCF of 1872 and$ 1320 = 2^3 \times 3 = 24$
Therefore, length of side of the square tile = 24cm
Area of the tile $= 24 \times 24 = 576cm^2$^
Number of tiles required $=\frac{\text{Area of courtyard}}{\text{Area of each tile}}$
$= \frac{2471040}{576} = 4290.$
Breadth of the yard $= 13m 20cm = 1300cm + 20cm = 1320cm$
Area of the yard $= 1872 \times 1320 = 2471040$
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 length and breadth
$1872 = 2^4 \times 3^2 \times 13$
$1320 = 2^3 \times 3 \times 5 \times 11$
HCF of 1872 and$ 1320 = 2^3 \times 3 = 24$
Therefore, length of side of the square tile = 24cm
Area of the tile $= 24 \times 24 = 576cm^2$^
Number of tiles required $=\frac{\text{Area of courtyard}}{\text{Area of each tile}}$
$= \frac{2471040}{576} = 4290.$
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