1. **Problem statement:** We have a kite ABCD with diagonals AC and DB intersecting at E such that AC is perpendicular to DB and DE = EB. We are given lengths AE = 8 cm, EC = 10 cm, and DE = EB = 12 cm. We need to find the length of AC. 2. **Important properties:** In a kite, the diagonals are perpendicular, and one diagonal (DB) is bisected by the other (AC). Since DE = EB, point E is the midpoint of DB. 3. **Calculate AC:** The length of AC is the sum of AE and EC: $$AC = AE + EC = 8 + 10 = 18 \text{ cm}$$ 4. **Final answer:** The length of AC is 18 cm. Note: The problem asks for the length of AC to the nearest tenth, so the answer is 18.0 cm.