1. **Problem statement:** Find the area of a park with width $\sqrt{15}$ meters and length $7\sqrt{21}$ meters. 2. **Formula:** The area $A$ of a rectangle is given by $$A = \text{length} \times \text{width}$$ 3. **Substitute the given values:** $$A = (7\sqrt{21}) \times (\sqrt{15})$$ 4. **Multiply the square roots:** $$A = 7 \times \sqrt{21 \times 15}$$ 5. **Calculate the product inside the square root:** $$21 \times 15 = 315$$ 6. **Simplify $\sqrt{315}$:** Factor 315 into prime factors: $$315 = 9 \times 35 = 3^2 \times 5 \times 7$$ So, $$\sqrt{315} = \sqrt{3^2 \times 5 \times 7} = 3\sqrt{35}$$ 7. **Substitute back:** $$A = 7 \times 3 \sqrt{35} = 21 \sqrt{35}$$ **Final answer:** $$\boxed{21 \sqrt{35} \text{ square meters}}$$