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