Question

How
many carpets of dimensions
3 m x 2 m are required to cover the floor
of hall, whose dimensions are
30 m x 12 m ?
a
B) 60
(A) 30
(C) 90
(D) 125​

Answer 1

Answer:

Hey..

60 is the answer..okk

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Answer 2

Answer:

$\red\bigstar$ There is a need of 60 carpets of dimensions 3 m x 2 m to cover the floor of hall, whose dimensions are 30 m x 12 m.

SOLUTION

FLOOR

The Floor of the room is of Rectangular Shape.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 30m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 12m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Length of the floor = 30m.

Breadth of the floor = 12m.

CARPET

The Carpet is also of rectangular shape.

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 3m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 2m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

Length of the carpet = 3m.

Breadth of the carpet = 2m.

$\boxed {\sf Number \: of \: Carpet \: Needed = \dfrac{Area \: of \: the \: floor}{Area \: of \: the \: Carpet} }$

Areas

1.Area of the the Floor

Area of a Rectangle = l × b (Length × Breadth)

Here,

Length(l) = 30m.

Breadth(b) = 12m.

Area of the floor = 30 × 12

$\implies$ Area of the floor = 360 m².

2.Area of the the Carpet

Area of a Rectangle = l × b (Length × Breadth)

Here,

Length(l) = 3m.

Breadth(b) = 2m.

Area of the Carpet = 3 × 2

$\implies$ Area of the Carpet = 6 m².

${\sf Number \: of \: Carpet \: Needed = \dfrac{Area \: of \: the \: floor}{Area \: of \: the \: Carpet} }$

$\implies {\sf Number \: of \: Carpet \: Needed = \dfrac{360}{6} }$

$\implies \boxed {\boxed{\boxed{\sf Number \: of \: Carpet \: Needed = 60}}}$