1. **State the problem:** Find the value of $x$ when the area of the rectangle is 10 cm². 2. **Formula for area of a rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ 3. **Assuming the rectangle's dimensions depend on $x$ (not explicitly given), let the length be $l(x)$ and width be $w(x)$.** 4. **Set up the equation:** $$l(x) \times w(x) = 10$$ 5. **Solve for $x$ using the given expressions for length and width (not provided in the prompt, so assume $l(x)$ and $w(x)$ are known).** 6. **Example:** If $l = x$ and $w = 5 - x$, then $$x(5 - x) = 10$$ $$5x - x^2 = 10$$ $$-x^2 + 5x - 10 = 0$$ 7. **Rewrite as:** $$x^2 - 5x + 10 = 0$$ 8. **Use quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=-5$, $c=10$. 9. **Calculate discriminant:** $$\Delta = (-5)^2 - 4 \times 1 \times 10 = 25 - 40 = -15$$ 10. **Since $\Delta < 0$, no real solutions exist for this example.** 11. **If actual expressions for length and width are given, substitute and solve similarly.** 12. **Final answer:** The value of $x$ that satisfies the area condition, rounded to 1 decimal place, depends on the specific expressions for length and width. --- **Note:** The user message contains multiple problems, but per instructions, only the first problem is solved here.