When a 50 decimeter long ladder is placed with the wall, it reaches upto the window only. If the window is 48 decimeter up from the land, then find out the distance of the lower face of the ladder from the wall.

Options

A. 12 decimeter
B. 14 decimeter
C. 10 decimeter
D. 11 decimeter

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Problem**: We have a ladder that is 50 decimeters long, leaning against a wall. The top of the ladder reaches a window that is 48 decimeters above the ground. We need to find the distance from the base of the ladder to the wall.

2. **Draw a Diagram**: Visualize the situation by drawing a right triangle. Let:
- The wall be represented as line segment AB (height = 48 dm).
- The ground be represented as line segment AC (the distance we need to find).
- The ladder be represented as line segment BC (length = 50 dm).

3. **Apply the Pythagorean Theorem**: In a right triangle, the relationship between the lengths of the sides is given by the Pythagorean theorem:
\[ BC^2 = AB^2 + AC^2 \]
Here, BC is the length of the ladder (50 dm), AB is the height of the window (48 dm), and AC is the distance from the wall (which we will denote as x).

4. **Substitute the Known Values**: Substitute the known values into the equation:
\[ 50^2 = 48^2 + x^2 \]

5. **Calculate the Squares**:
- Calculate \(50^2\):
\[ 50^2 = 2500 \]
- Calculate \(48^2\):
\[ 48^2 = 2304 \]

6. **Set Up the Equation**: Now substitute these values back into the equation:
\[ 2500 = 2304 + x^2 \]

7. **Isolate \(x^2\)**: To find \(x^2\), subtract 2304 from both sides:
\[ x^2 = 2500 - 2304 \]
\[ x^2 = 196 \]

8. **Take the Square Root**: To find \(x\), take the square root of both sides:
\[ x = \sqrt{196} \]
\[ x = 14 \text{ dm} \]

9. **Conclusion**: The distance of the lower face of the ladder from the wall is 14 decimeters.