1. **State the problem:** We have a triangle with sides labeled 15, 12, and 10, and two horizontal segments inside it labeled $y$ and 4 on the upper segment, and $x$ on the lower segment. We need to find the values of $x$ and $y$. 2. **Identify the relationships:** The segments inside the triangle are parallel to the base, so the triangles formed are similar. This means the ratios of corresponding sides are equal. 3. **Set up the ratios:** Using similarity, the ratio of the segment labeled $y$ to 4 equals the ratio of the side 15 to 12: $$\frac{y}{4} = \frac{15}{12}$$ 4. **Solve for $y$:** $$y = 4 \times \frac{15}{12}$$ Simplify the fraction: $$y = 4 \times \frac{\cancel{15}}{\cancel{12}} = 4 \times \frac{5}{4}$$ $$y = 5$$ 5. **Set up the ratio for $x$:** The segment $x$ corresponds to the side 10, so: $$\frac{x}{10} = \frac{15}{12}$$ 6. **Solve for $x$:** $$x = 10 \times \frac{15}{12}$$ Simplify the fraction: $$x = 10 \times \frac{\cancel{15}}{\cancel{12}} = 10 \times \frac{5}{4}$$ $$x = 12.5$$ **Final answers:** $$x = 12.5$$ $$y = 5$$