Question

how many of square tiles of side of 50 cm will be required to pave the floor of rectangular room 4m×3m
plz tell fast??​

Answer 1

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept Area of Square and Area of Rectangle has been used. First we will find the area of each tile and then we will find the area of the room. Finally the sum of areas of all required tiles will be equal to area of the floor of room. So to find number of tiles, we will divide the area of floor of room by area of each tile.

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★ Equations Used :-

$\\\;\large{\boxed{\sf{Area\;of\;Square\;=\;\bf{(Side)^{2}}}}}$

$\\\;\large{\boxed{\sf{Area\;of\;Rectangle\;=\;\bf{Length\;\times\;Breadth}}}}$

$\\\;\large{\boxed{\sf{n\;\times\;Area\;of\;Each\;Tile\;=\;\bf{Area\;of\;Floor}}}}$

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★ Solution :-

Given,

» Side of square tile = 50 cm = 0.5 m

» Dimensions of rectangular floor = 4 m × 3 m

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~ For the Area of Each Tile :-

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;Area\;of\;Square_{(Tile)}\;=\;\bf{(Side)^{2}}}$

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;Area\;of\;Square_{(Tile)}\;=\;\bf{(0.5)^{2}}}$

$\\\;\;\;\;\;\sf{:\rightarrow\;\;\;Area\;of\;Square_{(Tile)}\;=\;\underline{\underline{\bf{0.25\;\;m^{2}}}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;each\;\;Tile\;\;=\;\bf{0.25\;\;m^{2}}}}}$

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~ For the Area of Floor :-

$\\\;\;\;\;\;\sf{:\Longrightarrow\;\;\;Area\;of\;Rectangle_{(Floor)}\;=\;\bf{Length\;\times\;Breadth}}$

$\\\;\;\;\;\;\sf{:\Longrightarrow\;\;\;Area\;of\;Rectangle_{(Floor)}\;=\;\bf{4\;\times\;3}}$

$\\\;\;\;\;\;\sf{:\Longrightarrow\;\;\;Area\;of\;Rectangle_{(Floor)}\;=\;\underline{\underline{\bf{12\;\;m^{2}}}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;floor\;\;=\;\bf{12\;\;m^{2}}}}}$

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~ For the number of tiles required :-

✒ Let the number of tiles required be n. Then,

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;n\;\times\;Area\;of\;Each\;Tile\;=\;\bf{Area\;of\;Floor}}$

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;n\;\times\;0.25\;=\;\bf{12}}$

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;n\;=\;\bf{\dfrac{12}{0.25}}}$

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;n\;=\;\bf{\dfrac{12}{0.25}\;\times\;\dfrac{100}{100}}}$

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;n\;=\;\bf{\dfrac{1200}{25}}}$

$\\\;\;\;\;\;\sf{:\mapsto\;\;\;n\;=\;\underline{\underline{\bf{48}}}}$

$\\\;\large{\underline{\underline{\rm{Thus,\;number\;of\;tiles\;required\;are\;\;\boxed{\bf{48}}}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\\\;\sf{\leadsto\;\;\;Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\:\times\:Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;\;Perimeter\;of\;Square\;=\;4\;\times\;(Side)}$

$\\\;\sf{\leadsto\;\;\;Perimeter\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{\leadsto\;\;\;Perimeter\;of\;Circle\;=\;2 \pi r}$