Question

\large\underline{\sf{Solution-}}Solution−​ Dimensions of rectangular room Length of room = 45 cm Breadth of room = 25 cm Now, it is given that rectangular room measuring 45 cm by 25 cm is to be tiled using square tiles. So, edge of square tile = HCF (45, 25) Calculations of HCF of 45 and 25 Prime factorization of 45 = 3 × 3 × 5 Prime factorization of 25 = 5 × 5 It implies, HCF (45, 25) = 5 So, it means, edge of square tile = 5 cm. So, largest size of tile that can be used to tile the floor is 5 cm. Let assume that n number of tiles are needed to tile the floor, without cutting. \begin{gathered}\rm \: n \times Area_{(tile)} = Area_{(Room)} \\ \end{gathered}n×Area(tile)​=Area(Room)​​ \begin{gathered}\rm \: n \times {(5)}^{2} = 45 \times 25 \\ \end{gathered}n×(5)2=45×25​ \begin{gathered}\rm \: n \times 25 = 45 \times 25 \\ \end{gathered}n×25=45×25​ \begin{gathered}\rm\implies \:n \: = \: 45 \\ \end{gathered}⟹n=45​ Hence, 45 number of tiles are needed to tile the floor, without cutting. \rule{190pt}{2pt} Formulae Used :- \begin{gathered}\boxed{ \rm{ \:Area_{(Rectangle)} = Length \times breadth \: }} \\ \end{gathered}Area(Rectangle)​=Length×breadth​​ \begin{gathered}\boxed{ \rm{ \:Area_{(Square)} = {(side)}^{2} \: }} \\ \end{gathered}Area(Square)​=(side)2​​ \rule{190pt}{2pt} Additional information :- \begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}†FormulasofAreas:−​⋆Square=(side)2⋆Rectangle=Length×Breadth⋆Triangle=21​×Base×Height⋆Scalene△=s(s−a)(s−b)(s−c)​⋆Rhombus=21​×d1​×d2​⋆Rhombus=21​d4a2−d2​⋆Parallelogram=Base×Height⋆Trapezium=21​(a+b)×Height⋆EquilateralTriangle=43​​(side)2​​​​?​

Answer 1

Answer:

the same of 35 side 36 of base is 369.856 of the ratio of 3.6