Similar Triangles
1. The problem states that two triangles are similar, meaning their corresponding sides are proportional.
2. The first triangle has sides 2, 3, and 5. The second triangle has sides $x$, 6, and 10.
3. Since the triangles are similar, the ratios of corresponding sides are equal:
$$\frac{x}{2} = \frac{6}{3} = \frac{10}{5}$$
4. Simplify the known ratios:
$$\frac{6}{3} = 2 \quad \text{and} \quad \frac{10}{5} = 2$$
5. So, the ratio of similarity is 2. Therefore:
$$\frac{x}{2} = 2$$
6. Solve for $x$:
$$x = 2 \times 2 = 4$$
7. The value of $x$ is about 4, which corresponds to option a.