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The image shows a right triangle where the pond's width across is represented by \(x\), the unknown value we need to find. The triangle has two legs of lengths 150 feet and 250 feet.

This is a typical application of the Pythagorean Theorem, which states:

\[
a^2 + b^2 = c^2
\]

Where:
- \(a\) and \(b\) are the legs of the right triangle.
- \(c\) is the hypotenuse (in this case, \(x\)).

Here, one leg is 150 feet, and the other leg is 250 feet, so we can apply the formula as:

\[
x^2 = 150^2 + 250^2
\]

Now, let's calculate it step by step:

\[
x^2 = 150^2 + 250^2 = 22500 + 62500 = 85000
\]

\[
x = \sqrt{85000} \approx 291.5 \, \text{feet}
\]

So, the distance across the pond is approximately **291.5 feet**, rounded to the nearest tenth.

Would you like further details or clarifications?

Here are 5 related questions to consider:
1. How does the Pythagorean theorem apply to real-world problems?
2. Can we generalize the Pythagorean theorem for non-right triangles?
3. How would the solution change if the pond's shape was different, requiring different methods?
4. What are some practical applications of the Pythagorean theorem in fields like construction or navigation?
5. How can trigonometry be used to find missing sides in triangles not involving the Pythagorean theorem?

**Tip:** When solving right triangle problems, always ensure you correctly identify the hypotenuse as it is the longest side opposite the right angle.

Learn how to apply the Pythagorean Theorem to find the distance across a pond. In this example, the legs of the triangle are 150 ft and 250 ft, leading to a solution of approximately 291.5 ft. This problem is suitable for students in Grades 8-10.

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