The length of a room is (3x + 10) m and the breadth of the room is (2x + 5) m. The area of four walls of the room is (60x + 180) m². What is the height of the room?

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RRB NTPC Exam 19 Jan 2021 click here to view all questions

The length of a room is (3x + 10) m and the breadth of the room is (2x + 5) m. The area of four walls of the room is (60x + 180) m². What is the height of the room?

A4 m

B6 m

C7 m

D8 m

Akhilesh ? Apr 17 '25 at 21:36

correct answer is: option b [6 m]
Explanation: 

The length of the room is \( (3x + 10) \) m and the breadth is \( (2x + 5) \) m. The area of the four walls is given by:

\[ \text{Area} = 2 \times (\text{length} + \text{breadth}) \times \text{height} \]

\[ 60x + 180 = 2 \times ((3x + 10) + (2x + 5)) \times \text{height} \]

\[ 60x + 180 = 2 \times (5x + 15) \times \text{height} \]

\[ 60x + 180 = (10x + 30) \times \text{height} \]

\[ \text{height} = \frac{60x + 180}{10x + 30} = \frac{60(x + 3)}{10(x + 3)} = 6 \text{ m} \]

\(\boxed{6 \text{ m}}\)

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correct answer is: option b [6 m] Explanation:  The length of the room is \( (3x + 10) \) m and the breadth is \( (2x + 5) \) m. The area of the four walls is given by: \[ \text{Area} = 2 \times (\text{length} + \text{breadth}) \times \text{height} \] \[ 60x + 180 = 2 \times ((3x + 10) + (2x + 5)) \times \text{height} \] \[ 60x + 180 = 2 \times (5x + 15) \times \text{height} \] \[ 60x + 180 = (10x + 30) \times \text{height} \] \[ \text{height} = \frac{60x + 180}{10x + 30} = \frac{60(x + 3)}{10(x + 3)} = 6 \text{ m} \] \(\boxed{6 \text{ m}}\) Akhilesh ? answered Apr 17 '25 at 21:36

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