1. **Problem:** Find the length of the transverse axis of the ellipse given by $$\frac{x^2}{25} + \frac{y^2}{9} = 1$$ 2. **Formula and Explanation:** The standard form of an ellipse centered at the origin is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where: - $a$ is the semi-major axis if $a > b$ - $b$ is the semi-minor axis if $b < a$ The transverse axis length is $2a$ (the major axis length). 3. **Identify $a^2$ and $b^2$:** From the equation, $a^2 = 25$ and $b^2 = 9$. 4. **Calculate $a$:** $$a = \sqrt{25} = 5$$ 5. **Calculate the length of the transverse axis:** $$\text{Length} = 2a = 2 \times 5 = 10$$ **Final answer:** The length of the transverse axis is 10.