The area of the 4 walls of a room is `77 m^(2)`. The length and breadth of the room are 7.5 m and 3.5 m respectively. Find the height of the room.

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 rectangular room can be calculated using the formula:
\[ \text{Area} = 2 \times \text{Height} \times (\text{Length} + \text{Breadth}) \]

### Step 2: Substitute the known values into the formula
We know:
- Area = 77 m²
- Length = 7.5 m
- Breadth = 3.5 m

Substituting these values into the formula gives us:
\[ 77 = 2 \times h \times (7.5 + 3.5) \]

### Step 3: Calculate the sum of Length and Breadth
Calculate \(7.5 + 3.5\):
\[ 7.5 + 3.5 = 11 \]

### Step 4: Substitute the sum back into the equation
Now substitute back into the equation:
\[ 77 = 2 \times h \times 11 \]

### Step 5: Simplify the equation
This simplifies to:
\[ 77 = 22h \]

### Step 6: Solve for Height (h)
To find \(h\), divide both sides by 22:
\[ h = \frac{77}{22} \]

### Step 7: Simplify the fraction
Now simplify \(\frac{77}{22}\):
\[ h = \frac{77 \div 11}{22 \div 11} = \frac{7}{2} \]

### Step 8: Convert to decimal
Convert \(\frac{7}{2}\) to decimal:
\[ h = 3.5 \text{ m} \]

### Final Answer
The height of the room is \(3.5 \text{ m}\).

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