The question appears to involve a ladder leaning against a wall, where the ladder slides, and the new position of its base and its length are to be calculated using the Pythagorean theorem.

Question Analysis:

1. The ladder initially leans against the wall such that its base is 2.5 meters away from the wall.
2. After sliding, the base moves further, making it 1.4 meters farther from the wall, resulting in a total distance of 2.5 + 1.4 = 3.9 meters.
3. The top of the ladder slides down by 0.8 meters, meaning the vertical height of the ladder reduces.

The ladder forms a right triangle with:

• The new base distance = 3.9 meters
• The new height = $2.5 - 0.8 = 1.7$ meters

Using the Pythagorean theorem, the ladder's length $L$ is calculated as: $L = \sqrt{(\text{base})^2 + (\text{height})^2}$ $L = \sqrt{(3.9)^2 + (1.7)^2}$ $L = \sqrt{15.21 + 2.89} = \sqrt{18.1} \approx 6.5 \, \text{meters}$

The correct answer is therefore 6.5 meters.

Do you want further details or have any questions? Here are some related explorations:

1. What is the formula for the Pythagorean theorem and its applications?
2. How does the ladder's movement affect the triangle's geometry?
3. What are other practical uses of this concept in real life?
4. How can the formula for right triangles be extended to solve more complex shapes?
5. What if the ladder's length was fixed—how would that affect the calculations?

Tip: Visualize such problems using diagrams to better understand how dimensions relate geometrically!