1. **State the problem:** We have a rectangle with an area of 99 square units and a width of 11 units. We need to find the length of its diagonal, rounded to the nearest tenth. 2. **Recall the formulas:** - Area of a rectangle: $$\text{Area} = \text{length} \times \text{width}$$ - Diagonal of a rectangle (using Pythagorean theorem): $$d = \sqrt{\text{length}^2 + \text{width}^2}$$ 3. **Find the length:** Given area = 99 and width = 11, $$99 = \text{length} \times 11$$ Divide both sides by 11: $$\text{length} = \frac{99}{11} = 9$$ 4. **Calculate the diagonal:** Using $$d = \sqrt{\text{length}^2 + \text{width}^2}$$, $$d = \sqrt{9^2 + 11^2} = \sqrt{81 + 121} = \sqrt{202}$$ 5. **Simplify and round:** $$d \approx 14.2127$$ Rounded to the nearest tenth: $$d \approx 14.2$$ units **Final answer:** The length of the diagonal is approximately 14.2 units.