1. **State the problem:** We have an isosceles triangle with two equal sides of 15 units each and a base of 7x units. The perimeter is given as 17x units. 2. **Write the formula for the perimeter of a triangle:** $$\text{Perimeter} = \text{side}_1 + \text{side}_2 + \text{base}$$ 3. **Substitute the given values:** $$17x = 15 + 15 + 7x$$ 4. **Simplify the right side:** $$17x = 30 + 7x$$ 5. **This matches option (a):** $$17x = 30 + 7x$$ 6. **Solve for $x$:** Subtract $7x$ from both sides: $$17x - \cancel{7x} = 30 + \cancel{7x}$$ $$10x = 30$$ 7. **Divide both sides by 10:** $$\frac{10x}{\cancel{10}} = \frac{30}{\cancel{10}}$$ $$x = 3$$ **Final answer:** $x = 3$ and the correct equation is option (a) $17x = 30 + 7x$.