From the image provided, it looks like you're working with a right triangle. Here's a breakdown:

• The hypotenuse is labeled as $25$.
• One of the legs is labeled as $15$.
• The other leg is labeled as $x$.
• There is a right angle at $P$.

To solve for $x$, we can use the Pythagorean Theorem:
$a^2 + b^2 = c^2$ where:

• $c$ is the hypotenuse,
• $a$ and $b$ are the legs of the triangle.

Solution:

Let $a = x$, $b = 15$, and $c = 25$.

Substitute into the Pythagorean Theorem: $x^2 + 15^2 = 25^2$

Simplify: $x^2 + 225 = 625$

Subtract $225$ from both sides: $x^2 = 400$

Take the square root of both sides: $x = \sqrt{400}$ $x = 20$

Final Answer:

The length of $x$ is 20 units.

Do you have any questions or need further details? Here are some related questions to explore:

1. How do we verify the solution for $x$ using the Pythagorean Theorem?
2. What happens if one leg is missing instead of the hypotenuse?
3. How can trigonometry (sine, cosine, or tangent) be used to solve problems like this?
4. What are real-world applications of the Pythagorean Theorem?
5. How does the Pythagorean Theorem apply to non-right triangles?

Tip: Always double-check if the triangle is a right triangle before using the Pythagorean Theorem!