1. **State the problem:** We are given that the height of a door is 2.1 feet longer than its width, and the area of the door is 1675.8 square feet. We need to find the width and height of the door. 2. **Define variables:** Let the width be $w$ feet. 3. **Express height in terms of width:** Height $h = w + 2.1$ 4. **Write the area formula:** Area $A = \text{width} \times \text{height} = w \times h$ 5. **Substitute height into area formula:** $$1675.8 = w(w + 2.1)$$ 6. **Expand and form quadratic equation:** $$1675.8 = w^2 + 2.1w$$ Rearranged: $$w^2 + 2.1w - 1675.8 = 0$$ 7. **Use quadratic formula:** $$w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=2.1$, $c=-1675.8$ Calculate discriminant: $$\Delta = 2.1^2 - 4(1)(-1675.8) = 4.41 + 6703.2 = 6707.61$$ Calculate roots: $$w = \frac{-2.1 \pm \sqrt{6707.61}}{2} = \frac{-2.1 \pm 81.89}{2}$$ 8. **Find positive root (width must be positive):** $$w = \frac{-2.1 + 81.89}{2} = \frac{79.79}{2} = 39.895$$ 9. **Find height:** $$h = w + 2.1 = 39.895 + 2.1 = 41.995$$ 10. **Round to nearest tenth:** Width $w \approx 39.9$ feet Height $h \approx 42.0$ feet **Final answer:** The width of the door is approximately 39.9 feet and the height is approximately 42.0 feet.