Question

What will be the size largest square tile that can be used for the floorings

without cutting any tile for rectangular hall of size 24mX15m?​

Answer 1

$\huge{\mathcal{\blue{\underline{\underline{\pink{HeYa!!!}}}}}}$

${\huge{\purple{\mathbb{\bold{ANSWER}}}}}$

${\huge{\blue{\bold{\underline{Given:-}}}}}$

▪︎ Dimensions of hall = 24m×15m.

▪︎ Let the side of the tile be a.

${\large{\blue{\bold{\underline{Formula\:\:Used:-}}}}}$

▪︎ Area of rectangle,

= Length×Breadth.(L×B)

▪︎ Area of square

= Side×Side.(a)²

${\small{\blue{\bold{\underline{Area\:Of\:hall}}}}}$

= L × B.

= 24m × 15m.

= 360m².

${\large{\red{\boxed{\bold{=\:360m\:square}}}}}$

${\large{\blue{\bold{\underline{Now,}}}}}$

▪︎ The tile should be fix in the hall.

▪︎ Therefore its area should be less than the area of hall.

${\large{\blue{\bold{\underline{Therefore,}}}}}$

=》 a² < 360m².

=》 a < 18.97m.

{Approx}

${\large{\green{\boxed{\bold{=》\:a\:=\:18m.}}}}}$

Therefore the side or size of the largest square tile is equal to 18m.

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Answer 2

$\tt ฏGIVEN:−$

$\tt length \: of \: floor = 4m =400cm$

$\tt breadth\: of \: floor= 3m = 300cm$

$\tt length\: of \: single \: tile= 8cm$

$\tt breadth\: of \: single \: tile= 6cm$

$\tt ฏFIND:-$

$\tt no. \: of \: tiles \: reqire = ?$

$\tt ฏSOLUTION:-$

$\tt area \: of \: floor = 400 \times 30 \\ \tt = 120000 {cm}^{2}$

$\tt area \: of \: each \: tile= 8 \times 6 = 4 {cm}^{2}$

$\tt now \: let \: no. \: of \: tiles = x$

$\tt = > area \: of \:hall= x\times area \: of \: each$

$\tt = > 120000 = x(48)$

$\tt = > x = \frac{ \cancel{ 120000}}{ \cancel{48}} = 2500$

$\boxed{ \tt so \: total \: no. \: of \: tile \: is \boxed{2500}}$