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 follow these steps:

### Step 1: Understand the problem
We have two buildings:
- Building I (height = 19 m)
- Building II (height = 40 m)
The horizontal distance between the two buildings is 20 m.

### Step 2: Visualize the scenario
Draw a diagram with:
- Point A at the base of Building I.
- Point B at the top of Building I (height = 19 m).
- Point C at the base of Building II (20 m away from A).
- Point D at the top of Building II (height = 40 m).

### Step 3: Determine the vertical distance between the tops of the buildings
The vertical distance between the tops of the buildings (from point B to point D) can be calculated as follows:
- Height of Building II (D) - Height of Building I (B) = 40 m - 19 m = 21 m.

### Step 4: Create a right triangle
We can form a right triangle with:
- The horizontal distance (base) = 20 m (distance between the two buildings).
- The vertical distance (height) = 21 m (difference in height between the tops of the buildings).

### Step 5: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ BD^2 = BM^2 + MD^2 \]
Where:
- \( BD \) is the distance between the tops of the buildings.
- \( BM \) is the horizontal distance = 20 m.
- \( MD \) is the vertical distance = 21 m.

Substituting the values:
\[ BD^2 = 20^2 + 21^2 \]
Calculating:
\[ BD^2 = 400 + 441 = 841 \]

### Step 6: Calculate the distance
Now, take the square root to find \( BD \):
\[ BD = \sqrt{841} = 29 \text{ m} \]

### Final Answer
The distance between the tops of the two buildings is **29 meters**.

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