Two building I and II are of heights 19 m and 40 m respectively 20 m apart. The distance between their tops is:

Options

A. `sqrt(1961)m`
B. `sqrt(802)m`
C. 29 m
D. 41 m

Answer

To find the distance between the tops of two buildings of heights 19 m and 40 m that are 20 m apart, we can use the Pythagorean theorem. Here’s how to solve the problem step by step:

### Step 1: Identify the heights of the buildings
Let the height of Building I be \( h_1 = 19 \) m and the height of Building II be \( h_2 = 40 \) m.

### Step 2: Calculate the difference in heights
The difference in height between the two buildings is:
\[ \Delta h = h_2 - h_1 = 40 \, \text{m} - 19 \, \text{m} = 21 \, \text{m} \]

### Step 3: Form a right triangle
We can visualize the situation as a right triangle where:
- One leg is the horizontal distance between the buildings, which is \( 20 \) m.
- The other leg is the difference in height between the tops of the buildings, which is \( 21 \) m.

### Step 4: Apply the Pythagorean theorem
According to the Pythagorean theorem, the distance \( d \) between the tops of the buildings can be calculated using:
\[ d = \sqrt{(20 \, \text{m})^2 + (21 \, \text{m})^2} \]

### Step 5: Calculate the squares
Calculating the squares of the legs:
\[ (20 \, \text{m})^2 = 400 \, \text{m}^2 \]
\[ (21 \, \text{m})^2 = 441 \, \text{m}^2 \]

### Step 6: Sum the squares
Now, add the squares:
\[ 400 \, \text{m}^2 + 441 \, \text{m}^2 = 841 \, \text{m}^2 \]

### Step 7: Take the square root
Finally, take the square root to find the distance:
\[ d = \sqrt{841 \, \text{m}^2} = 29 \, \text{m} \]

### Conclusion
The distance between the tops of the two buildings is \( 29 \) m.

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