To solve this problem, we can use the Pythagorean theorem. Here's the step-by-step approach:

1. First scenario (ladder on one side of the street):

In the first situation, the ladder is leaning against the window which is 7 meters above the ground. This forms a right-angled triangle where:

• The ladder is the hypotenuse, which is 25 meters long.
• The height of the window is 7 meters (opposite side).
• The distance from the wall (the horizontal distance) is unknown.

Using the Pythagorean theorem: $\text{hypotenuse}^2 = \text{height}^2 + \text{distance}^2$ Substituting the known values: $25^2 = 7^2 + d^2$ $625 = 49 + d^2$ $d^2 = 625 - 49 = 576$ $d = \sqrt{576} = 24 \text{ meters}$ So, the distance from the base of the ladder to the wall is 24 meters.

2. Second scenario (ladder on the other side of the street):

In the second situation, the ladder is turned to the other side of the street to reach a window at a height of 24 meters. We now have:

• The ladder is still 25 meters long (same hypotenuse).
• The height of the window is 24 meters (opposite side).
• The distance from the wall (horizontal distance) is unknown, but this will be the same as the width of the street.

Using the Pythagorean theorem again: $25^2 = 24^2 + w^2$ $625 = 576 + w^2$ $w^2 = 625 - 576 = 49$ $w = \sqrt{49} = 7 \text{ meters}$

Thus, the width of the street is 7 meters.

Final Answer:

The width of the street is 7 meters.

Would you like more details or any clarifications? Here are some related questions:

1. How would the answer change if the height of the second window was less than the first window?
2. What if the ladder's length was different? How would that affect the width?
3. How can we apply the Pythagorean theorem to other real-life problems?
4. Could this problem be solved using trigonometric functions instead of the Pythagorean theorem?
5. How do we calculate the angle of elevation of the ladder in both situations?

Tip: Always remember to check whether you’re dealing with a right triangle, as the Pythagorean theorem only applies in such cases.