The length of longest pole that can be placed on the floor of a room is 12 m and the length of longest pole that cn be placed in the room is 15 m . The height of the room is :

Options

A. 3m
B. 6m
C. 9m
D. none of these

Answer

To find the height of the room based on the given information about the lengths of the longest poles, we can follow these steps:

### Step 1: Understand the problem
We have two lengths provided:
1. The length of the longest pole that can be placed on the floor of the room (which is the diagonal of the floor) is 12 m.
2. The length of the longest pole that can be placed in the room (which is the diagonal of the room) is 15 m.

### Step 2: Set up the equations
Let:
- \( L \) = length of the room
- \( B \) = breadth of the room
- \( H \) = height of the room

From the first piece of information, we can use the Pythagorean theorem for the diagonal of the floor:
\[ L^2 + B^2 = 12^2 \]
\[ L^2 + B^2 = 144 \quad \text{(Equation 1)} \]

From the second piece of information, we can use the Pythagorean theorem for the diagonal of the room:
\[ L^2 + B^2 + H^2 = 15^2 \]
\[ L^2 + B^2 + H^2 = 225 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 1 into Equation 2
From Equation 1, we know that \( L^2 + B^2 = 144 \). We can substitute this into Equation 2:
\[ 144 + H^2 = 225 \]

### Step 4: Solve for \( H^2 \)
Now, we can isolate \( H^2 \):
\[ H^2 = 225 - 144 \]
\[ H^2 = 81 \]

### Step 5: Find \( H \)
To find the height \( H \), we take the square root of both sides:
\[ H = \sqrt{81} \]
\[ H = 9 \text{ m} \]

### Conclusion
The height of the room is 9 meters.

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