1. **Problem statement:** We have an isosceles triangle with a base of length $2$ cm and a perimeter of $10$ cm. We need to find the length of the two equal sides. 2. **Formula and explanation:** The perimeter $P$ of a triangle is the sum of all its sides. For an isosceles triangle with equal sides of length $x$ and base $b$, the perimeter is: $$P = 2x + b$$ 3. **Substitute known values:** Here, $P = 10$ cm and $b = 2$ cm, so: $$10 = 2x + 2$$ 4. **Solve for $x$:** Subtract $2$ from both sides: $$10 - 2 = 2x$$ $$8 = 2x$$ Divide both sides by $2$: $$x = \frac{8}{2} = 4$$ 5. **Answer:** The length of each equal side is $4$ cm.