Question
A rectangular courtyard is $18m, 72\ cm$ long and $13m, 20\ cm$ board. It is to be paved with square tiles of the same size. Find the least possibele number of such tiles.
✓
Answer
Length of the courtyard $= 18m, 72\ cm = 1872\ cm$
Breadth of the courtyard $= 13m, 20\ cm = 1320\ cm$
Now, maximum edge of the square tile is given by the $HCF$ of $1872\ cm$ and $1320\ cm.$
$HCF$ of $1872$ and $1320 = 24$
$\therefore$ maximum edge of the squre tile $= 24\ cm$
Required number of tiles $=\frac{\text{area of courtyard}}{\text{area of each square tile}}$
$=\frac{1872\times1320}{24\times24}$
$=4290$
Breadth of the courtyard $= 13m, 20\ cm = 1320\ cm$
Now, maximum edge of the square tile is given by the $HCF$ of $1872\ cm$ and $1320\ cm.$
$HCF$ of $1872$ and $1320 = 24$
$\therefore$ maximum edge of the squre tile $= 24\ cm$
Required number of tiles $=\frac{\text{area of courtyard}}{\text{area of each square tile}}$
$=\frac{1872\times1320}{24\times24}$
$=4290$
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