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Area Calculation MCQ 4: ( Width of carpet given, to find length of the carpet to cover a rectangular room)

Area Calculation MCQ 4: How many meters of carpet 63 cm wide will be required to cover the floor of the room 14 m by 9 m ?

a) 200            b) 220                 c) 210              d) 185

Solution:

In this question we are given following data;

Width of room =W= 9 m

Length of room =L= 14 m

Width of carpet =w= 63 cm = 0.63 m

Length of carpet = l=?

From this data we can infer that room is rectangular – and area of a rectangle is ;

\[ Area Of Rectangle = Length\times Width \]

So, area of given room is;

\[ Area Of Room= 14\times9=126 m^2 \]

or

\[ L\times W= 14\times9=126 m^2 \]

drawit diagram 10

or

\[ L\times W=126m^2 —-(1 \]

And area of carpet to cover rectangle made by the room is;

\[ Area Of Carpet=l\times w \]

Since carpet will cover the room so area of carpet and room will be equal or same i-e;

\[ Area Of Carpet = Area Of Room \]

or

\[ l\times w= L\times W \]

Putting values of ‘w’ and ‘LxW’ from eq 1, we get;

\[ l\times 0.63= 126 \]

or

\[ l=\frac{126}{0.63}=200 m \]

drawit diagram 9

 

So the length of carpet will be 200 meters, This carpet of length 200 m and width 0.63 m will be cut into 200/14= 14.285714286 m  – each stripe length- to cover the room by placing these side by side.

So option  a  is correct !

 

 

 

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