Eli is building a slide for his kids. If the ladder is 1 meter tall and he wants the bottom of the slide to be 4 meters from the ladder, how long does the slide need to be? If necessary, round to the nearest tenth.

To find the length of the slide, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case:
- The ladder height is 1 meter, which is one leg of the triangle.
- The distance from the bottom of the ladder to the bottom of the slide is 4 meters, which is the other leg of the triangle.
- The length of the slide is the hypotenuse.

The Pythagorean theorem is given by:

\[
c = \sqrt{a^2 + b^2}
\]

Where:
- \(a = 1 \, \text{meter}\)
- \(b = 4 \, \text{meters}\)
- \(c\) is the length of the slide.

Plugging in the values:

\[
c = \sqrt{1^2 + 4^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.1 \, \text{meters}
\]

So, the slide needs to be approximately **4.1 meters** long.

Would you like more details or have any questions?

Here are some related questions to consider:
1. What is the significance of the Pythagorean theorem in real-life applications?
2. How would the slide length change if the ladder height was increased?
3. What if the ladder was positioned closer to the bottom of the slide?
4. How does rounding affect the final answer in problems like these?
5. Can you calculate the area of the triangle formed by the ladder, slide, and the ground?

**Tip:** Always double-check your triangle dimensions to ensure that the Pythagorean theorem applies correctly.

Discover how to calculate the length of a slide using the Pythagorean theorem. Given a ladder height of 1 meter and the bottom of the slide 4 meters away from the ladder, find out the exact slide length. Suitable for Grades 7-9.

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