The diagram shows a right triangle. Based on the image:

• One leg is labeled as $x$.
• The other leg is labeled as $2x$.
• The hypotenuse is labeled as $18$.

This appears to be a problem requiring the Pythagorean theorem, which states: $a^2 + b^2 = c^2$ where $a$ and $b$ are the legs, and $c$ is the hypotenuse.

Solution:

Using the Pythagorean theorem: $x^2 + (2x)^2 = 18^2$

1. Expand $(2x)^2$: $x^2 + 4x^2 = 324$

2. Combine like terms: $5x^2 = 324$

3. Solve for $x^2$: $x^2 = \frac{324}{5} = 64.8$

4. Take the square root to find $x$: $x = \sqrt{64.8} \approx 8.05$

Thus:

• $x \approx 8.05$
• The other leg $2x \approx 16.1$.

Let me know if you'd like a detailed explanation or if you have any questions!

Follow-up Questions:

1. How is the Pythagorean theorem applied to solve right triangles?
2. Why is the hypotenuse always the longest side in a right triangle?
3. Can the values of $x$ and $2x$ be verified further using trigonometric ratios?
4. What happens if the hypotenuse is replaced with another value?
5. How can similar triangles help solve right-triangle problems?

Tip: Always double-check units and ensure the triangle follows right-angle properties before applying the Pythagorean theorem.