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Q.

The perimeter of a floor of a room is 30 m   and its height is 3 m  . Find the area of four walls of the room.


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a

67 m 2  

b

45 m 2  

c

90 m 2  

d

34 m 2   

answer is C.

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Detailed Solution

It is given floor of perimeter 30 m and height 3 m.
Since, we have to find the surface area of the four walls of the room, we subtract the area of the ceiling and the base of the room.
Let the surface area of the four walls of the room be denoted by C.
Area of the ceiling of the room = l×b   Similarly, the area of the floor of the room  =l×b  
⇒   The surface area of four walls of the room = S−(l×b+l×b)  
⇒C=2(lb+bh+hl)−2lb  
⇒C=2lb+2bh+2hl−2lb   ⇒C=2(bh+hl)  
Take h   common from the bracket.
∴C=h×2(l+b)       … (1)
Given the perimeter of the floor of the room is 30 m.
The perimeter of the floor is given by the formula  2(l+b)  .
⇒2(l+b)=30         … (2)
Substitute the value from the equation (2) in equation (1).
⇒C=h×30   By substituting value of h,
⇒C=3×30  
⇒C=90 m 2  
Therefore, the surface area of the four walls of the room is 90  m 2   .
Hence option (3) is correct.
 
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The perimeter of a floor of a room is 30 m   and its height is 3 m  . Find the area of four walls of the room.