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The length of a room exceeds its breadth by 2 metres. If the length is increased by 4 metres and the breadth is decreased by 2 metres, the area remains the same. Find the surface area of its walls if the height is 3 metres.
  • a)
    248 m2
  • b)
    424 m2
  • c)
    112 m2
  • d)
    84 m2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The length of a room exceeds its breadth by 2 metres. If the length i...
The first step to solving this problem is to set up the equations based on the information given:

Let the length of the room be L metres and the breadth be B metres.

Given that the length exceeds the breadth by 2 metres, we have:
L = B + 2

When the length is increased by 4 metres and the breadth is decreased by 2 metres, the area remains the same:
(L + 4)(B - 2) = LB

Now, we can substitute the value of L from the first equation into the second equation and solve for B.

After finding the values of L and B, we can calculate the surface area of the walls of the room. The surface area of the walls can be calculated using the formula:
2h(L + B)

Given that the height of the room is 3 metres, we can substitute the values of L, B, and h into the formula and calculate the surface area of the walls.

Therefore, the correct answer is option 'D' - 84 m2.
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Community Answer
The length of a room exceeds its breadth by 2 metres. If the length i...
Let the breadth (b) of the room be 'x' metres
Then, length (l) of the room = (x + 2) metres
Area (A) = l × b = x(x + 2) m2
Given, length is increased by 4 metres and the breadth is decreased by 2 metres
Then, new length (l') of the room = (x + 6) metres
New breadth (b') of the room = (x - 2) metres
New Area (A') of the room = l' × b' = (x + 6) (x - 2) m2
Also given that, A = A'
Or x (x + 2) = (x + 6) (x - 2)
x2 + 2x = x2 + 4x - 12
2x = 12
x = 6
Therefore, the length of the room (l) = 8 metres
And breadth of the room (b) = 6 metres
And given height of the room (h) = 3 metres
Since the room will be in the shape of a cuboid,
Surface area of walls = 2(l + b)h
= 2(8 + 6)3 m2
= 84 m2
Hence, answer option 4 is correct.
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Each question is followed by two statements, A and B. Answer each question using the following instructions:Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.Mark option (3) if the question can be answered by using either statement alone.Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.Mark option (5) if the question cannot be answered on the basis of the two statements.Q. If the breadth of a rectangle is increased by 2 units and the length is decreased by 3 units, the area is unchanged. What is the area of the rectangle?A. If the breadth is decreased by 1 unit and the length is increased by 3 units, the area remains the same.B. If the breadth is increased by 1 unit and the length is increased by 2 units, the area gets doubled.

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The length of a room exceeds its breadth by 2 metres. If the length is increased by 4 metres and the breadth is decreased by 2 metres, the area remains the same. Find the surface area of its walls if the height is 3 metres.a)248 m2b)424 m2c)112 m2d)84 m2Correct answer is option 'D'. Can you explain this answer?
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