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?

Options

A. 4 m
B. 6 m
C. 7m
D. 8 m

Answer

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of the room (L) = \(3x + 10\) m
- Breadth of the room (B) = \(2x + 5\) m
- Area of the four walls (A) = \(60x + 180\) m²

2. **Use the formula for the area of the four walls:**
The formula for the area of the four walls of a room is given by:
\[ A = 2h(L + B) \]
where \(h\) is the height of the room.

3. **Substitute the known values into the formula:**
\[ 60x + 180 = 2h((3x + 10) + (2x + 5)) \]

4. **Simplify the expression inside the parentheses:**
\[ L + B = (3x + 10) + (2x + 5) = 5x + 15 \]
So, the equation becomes:
\[ 60x + 180 = 2h(5x + 15) \]

5. **Distribute \(2h\) on the right side:**
\[ 60x + 180 = 10hx + 30h \]

6. **Rearrange the equation:**
We can set both sides equal to each other:
\[ 60x + 180 = 10hx + 30h \]

7. **Equate the coefficients:**
For the equation to hold true for all values of \(x\), the coefficients of \(x\) and the constant terms must be equal:
- Coefficient of \(x\): \(60 = 10h\)
- Constant term: \(180 = 30h\)

8. **Solve for \(h\) using the coefficient of \(x\):**
\[ 10h = 60 \implies h = \frac{60}{10} = 6 \]

9. **Verify using the constant term:**
\[ 30h = 180 \implies h = \frac{180}{30} = 6 \]

10. **Conclusion:**
The height of the room is \(h = 6\) meters.