1. **Problem:** Given two similar triangles $\triangle SRT \sim \triangle CBD$, find the value of $x$ where sides correspond as follows: $SR = 11x - 4$, $RT = 70$, $CB = 60$, $BD = 50$, and $CD = 70$. 2. **Formula and rules:** For similar triangles, corresponding sides are proportional. That means: $$\frac{SR}{CB} = \frac{RT}{CD} = \frac{ST}{BD}$$ 3. **Set up proportion:** Using the sides given, $$\frac{11x - 4}{60} = \frac{70}{70}$$ 4. **Simplify right side:** $$\frac{70}{70} = 1$$ 5. **Solve for $x$:** $$\frac{11x - 4}{60} = 1$$ Multiply both sides by 60: $$\cancel{60} \times \frac{11x - 4}{\cancel{60}} = 1 \times 60$$ $$11x - 4 = 60$$ 6. **Isolate $x$:** $$11x = 60 + 4$$ $$11x = 64$$ $$x = \frac{64}{11}$$ 7. **Final answer:** $$x = \frac{64}{11} \approx 5.82$$ This means the value of $x$ that makes the triangles similar is approximately 5.82.