A ladder, `25` m long reaches a window of building `20` m, above the ground. The distance of the foot of the ladder from the building.

Options

A. `45` m
B. `5` m
C. `10` m
D. `15` m

Explanation

To solve the problem of finding the distance of the foot of the ladder from the building, we can use the Pythagorean theorem. Here’s the step-by-step solution:

### Step 1: Understand the problem
We have a right triangle formed by the ladder, the wall of the building, and the ground. The ladder acts as the hypotenuse, the height of the window is one leg, and the distance from the foot of the ladder to the building is the other leg.

### Step 2: Identify the lengths
- Length of the ladder (hypotenuse, AB) = 25 m
- Height of the window (one leg, AC) = 20 m
- Distance from the foot of the ladder to the building (the other leg, BC) = ?

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AB^2 = AC^2 + BC^2 \]
Where:
- \( AB \) is the length of the ladder (25 m)
- \( AC \) is the height of the window (20 m)
- \( BC \) is the distance we need to find

### Step 4: Substitute the known values
Substituting the known values into the equation:
\[ 25^2 = 20^2 + BC^2 \]

### Step 5: Calculate the squares
Calculating the squares:
\[ 625 = 400 + BC^2 \]

### Step 6: Rearrange the equation to solve for BC
Now, rearranging the equation to isolate \( BC^2 \):
\[ BC^2 = 625 - 400 \]
\[ BC^2 = 225 \]

### Step 7: Take the square root
Now, take the square root of both sides to find \( BC \):
\[ BC = \sqrt{225} \]
\[ BC = 15 \]

### Step 8: Conclusion
The distance of the foot of the ladder from the building is:
\[ \text{Distance} = 15 \text{ m} \]

### Final Answer
The distance of the foot of the ladder from the building is **15 meters**.

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