Question

11. 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 1

Answer: Least possible will be=78×55=4290

Step-by-step explanation:

length= 1872cm

breadth=1320cm

HCF of [1872,1320] =24cm

Side of each square=24cm.

Number of square tiles paved along length= 78

Number of square tiles paved along breadth=55

Least possible will be=78×55=4290

Answer 2

${\huge {\green{\underline{\underline\mathbb\red {Answer:-}}}}} </p><p>$

${ \underline{\underline {\mathtt\pink{Given :-}}}}</p><p>$

$\mathtt{Length \: of \: courtyard = 18m \: 72cm = 1872cm }\\ </p><p> \mathtt{Breadth \: of \: courtyard = 13 m \: 20 cm = 1320 cm}</p><p></p><p>$

${\underline{\underline \mathtt\blue{Formula \: to \: be \: used :-}}}</p><p></p><p> \boxed {\mathtt{ \frac{Number of tiles Area of courtyard}{Area of side of tile.}}}$

${\underline {\underline\mathtt \purple{Solution :-}}}</p><p> \mathtt{Taking \: out HCF \: of \: 1872 and \: 1320 } \\ \mathtt {using \: Euclid's \: Lemma, \: we get}$

$\implies \mathtt{1817 = 1320 × 1 + 552} \\ \implies \mathtt</p><p> {1320 = 552 × 2 + 216 } \\ \implies \mathtt {552 = 216 × 2 + 120} \\ \implies \mathtt{216 = 120 × 1 + 96} \\ \implies \mathtt{120 = 96 × 1 +24} \\ { \purple{ \fbox{\boxed{\implies \mathtt{96 = 24 × 4 + 0}}}}}$

$\mathtt{HCF \: of \: 1872 \: and \: 1320 {= 24}}\\ </p><p> \mathtt{Number \: of \: tiles { = \frac {Area \: of \: courtyard}{Area of \: side \: of tile }} }\\ </p><p> \mathtt{Number \: of \: tiles = \frac{1872 × 1320 }{24 × 24 }}\\ </p><p> {\red {\fbox{\boxed{\mathtt{Number \: of \: tiles = 4290}}}}}</p><p>$

Hence, the least possible number of such tiles are 4290.