Area of four walls of a room `75m^2`. The length and breadth of the room are 11.5 m and 3.5 m respectively. The height of the room is :

Options

A. 7.7m
B. 2.5m
C. 6.77m
D. 5.4m

Answer

To find the height of the room given the area of the four walls, we can follow these steps:

### Step 1: Understand the formula for the area of the four walls
The area of the four walls of a room can be calculated using the formula:
\[ \text{Area of 4 walls} = 2 \times \text{height} \times (\text{length} + \text{breadth}) \]

### Step 2: Substitute the known values into the formula
We know:
- Area of the four walls = 75 m²
- Length = 11.5 m
- Breadth = 3.5 m

Substituting these values into the formula gives us:
\[ 75 = 2 \times h \times (11.5 + 3.5) \]

### Step 3: Calculate the sum of length and breadth
Now, calculate the sum of the length and breadth:
\[ 11.5 + 3.5 = 15 \]

### Step 4: Rewrite the equation with the calculated sum
Now, substitute the sum back into the equation:
\[ 75 = 2 \times h \times 15 \]

### Step 5: Simplify the equation
We can simplify this equation:
\[ 75 = 30h \]

### Step 6: Solve for height (h)
To find the height, divide both sides of the equation by 30:
\[ h = \frac{75}{30} \]
\[ h = 2.5 \text{ m} \]

### Conclusion
The height of the room is **2.5 m**.

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