A 120 m long ladder reached a window 72 m from the ground on placing it against a wall. Find the distance of the foot of the ladder from the wall.

Options

A. 85 m
B. 92 m
C. 96 m
D. 82 m

Answer

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

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

### Step 2: Identify the lengths
- Length of the ladder (hypotenuse, AB) = 120 m
- Height of the window (one leg, AC) = 72 m
- Distance from the wall (the other leg, BC) = ?

### Step 3: Apply the Pythagorean theorem
According to the Pythagorean theorem:
\[ AB^2 = AC^2 + BC^2 \]
Substituting the known values:
\[ 120^2 = 72^2 + BC^2 \]

### Step 4: Calculate the squares
Calculate \( 120^2 \) and \( 72^2 \):
\[ 120^2 = 14400 \]
\[ 72^2 = 5184 \]

### Step 5: Substitute and solve for \( BC^2 \)
Now substitute these values into the equation:
\[ 14400 = 5184 + BC^2 \]
To find \( BC^2 \), rearrange the equation:
\[ BC^2 = 14400 - 5184 \]

### Step 6: Perform the subtraction
Calculate \( 14400 - 5184 \):
\[ BC^2 = 14400 - 5184 = 9216 \]

### Step 7: Take the square root
Now, take the square root of both sides to find \( BC \):
\[ BC = \sqrt{9216} \]
Calculating the square root:
\[ BC = 96 \]

### Step 8: Conclusion
The distance of the foot of the ladder from the wall is **96 meters**.

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