1. **State the problem:** We have a kite with four sides: two sides each of length $n$ cm and two sides each of length $n + 3$ cm. The perimeter is given as 102 cm. 2. **Formula for perimeter of a kite:** The perimeter $P$ is the sum of all side lengths. Since the kite has two sides of length $n$ and two sides of length $n + 3$, the perimeter is: $$P = n + n + (n + 3) + (n + 3)$$ 3. **Simplify the expression:** $$P = 2n + 2(n + 3) = 2n + 2n + 6 = 4n + 6$$ 4. **Set the perimeter equal to 102 and solve for $n$:** $$4n + 6 = 102$$ 5. **Isolate $n$ by subtracting 6 from both sides:** $$4n + \cancel{6} - \cancel{6} = 102 - 6$$ $$4n = 96$$ 6. **Divide both sides by 4 to solve for $n$:** $$\frac{4n}{\cancel{4}} = \frac{96}{\cancel{4}}$$ $$n = 24$$ **Final answer:** The value of $n$ is 24 cm.