1. **State the problem:** We need to find the value of $x$ given a right triangle where the vertical side is labeled $3x + 6$ and the horizontal side is labeled $30$. 2. **Understand the problem:** Since the triangle has two right angles and the hypotenuse has equal angles on each side, it suggests the triangle is isosceles right triangle, meaning the two legs are equal. 3. **Set up the equation:** Because the two legs are equal in an isosceles right triangle, we have: $$3x + 6 = 30$$ 4. **Solve for $x$:** Subtract 6 from both sides: $$3x = 30 - 6$$ $$3x = 24$$ Divide both sides by 3: $$x = \frac{24}{3}$$ $$x = 8$$ 5. **Conclusion:** The value of $x$ is 8.