Question

A rectangular floor which is 10.5 m long and 7.5 metre wide has to be covered by identical square tiles. find the least number of tiles required for paving the floor.

Answer 1

$\large{\red{ \bf{ \underline {\underline{Answer}}}}} \\ \\ \purple{ \sf{\mapsto 35 \: Tiles}} \\ \\ \mathrm{\green{ \underline{Given}}} \\ \\ \sf{ \rightsquigarrow Floor \: Length = 10.5 \: m} \\ \\ \sf{ \rightsquigarrow Width = 7.5 \: m}\\ \\ \mathrm {\blue{ \underline{ To \: Find}}} \\ \\ \sf{ \rightsquigarrow Number \: of \: Tiles\:=\:?}$

⠀⠀

❍ According To Given Question

⠀⠀

$\sf{Length \: of \: Floor = 10.5 \: m = 1050 \: cm} \\ \\ \sf{Width \: of \: Floor = 7.5 m = 750cm} \\ \\ \sf{So, \: 1050 = 2 \times 5 \times 5 \times 21} \\ \\ \sf{\dashrightarrow 2 \times 5 \times 5 \times 3 \times 7 } \\ \\ \sf{And \: 750 = 2 \times 3 \times 5 \times 5 \times 5} \\ \\ \sf{So, \: HCF \: of \: 1050 \: and \: 750} \\ \\ \sf{\dashrightarrow 2 \times 3 \times 5 \times 5} \\ \\ \sf{\dashrightarrow 150 \: cm} \\ \\ \sf{\dashrightarrow 1.5 \: m} \\ \\ \sf{So, \: side \: of \: tiles \:should \: be \: 1.5 \: m } \\ \\ \sf{So, \: Area \: of \: floor = 10.5 \times 7.5} \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \:\: \: = {78.75 \: m}^{2} } \\ \\ \sf{ \: \: \: \: \: \: \: Area \: of \: tiles = {(1.5)}^{2} } \\ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {2.25 \: m}^{2} } \\ \\ \sf{So, \: number \: of \: tiles = \frac{78.75}{2.25} } \\ \\ \purple{\dashrightarrow}\:\: \purple {\underline{ \boxed{ \sf{35 \: Tiles}}}}\:\: \Large{\orange{\dag}}$