The distance between the tops of two building 38 metres and 58 metres high is 52 metres. What will be the distance (in metres) between two buildings?

Options

A. 46
B. 42
C. 44
D. 48

Answer

To find the distance between the two buildings, we can use the Pythagorean theorem. The heights of the buildings and the distance between their tops form a right triangle.

### Step-by-Step Solution:

1. **Identify the heights of the buildings**:
- Building A height = 38 meters
- Building B height = 58 meters

2. **Calculate the difference in height**:
- Difference in height = Height of Building B - Height of Building A
- Difference = 58 m - 38 m = 20 m

3. **Use the Pythagorean theorem**:
- Let the distance between the two buildings be \( d \).
- According to the Pythagorean theorem:
\[ (Difference \ in \ height)^2 + d^2 = (Distance \ between \ tops)^2 \]
- Plugging in the values:
\[ (20)^2 + d^2 = (52)^2 \]
- This simplifies to:
\[ 400 + d^2 = 2704 \]

4. **Solve for \( d^2 \)**:
- Rearranging gives:
\[ d^2 = 2704 - 400 \]
\[ d^2 = 2304 \]

5. **Calculate \( d \)**:
- Taking the square root of both sides:
\[ d = \sqrt{2304} = 48 \text{ meters} \]

### Final Answer:
The distance between the two buildings is **48 meters**.