1. **State the problem:** We are given the area of a playground as 504 square yards. The length is expressed as $x + 8$ and the width as $x - 2$. We need to find the values of length and width. 2. **Write the formula for area of a rectangle:** $$\text{Area} = \text{Length} \times \text{Width}$$ 3. **Set up the equation:** $$504 = (x + 8)(x - 2)$$ 4. **Expand the right side:** $$504 = x^2 - 2x + 8x - 16$$ $$504 = x^2 + 6x - 16$$ 5. **Bring all terms to one side to form a quadratic equation:** $$x^2 + 6x - 16 - 504 = 0$$ $$x^2 + 6x - 520 = 0$$ 6. **Solve the quadratic equation using the quadratic formula:** The quadratic formula is: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=6$, and $c=-520$. 7. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 6^2 - 4(1)(-520) = 36 + 2080 = 2116$$ 8. **Calculate the square root of the discriminant:** $$\sqrt{2116} = 46$$ 9. **Find the two possible values for $x$:** $$x = \frac{-6 \pm 46}{2}$$ 10. **Calculate each root:** $$x_1 = \frac{-6 + 46}{2} = \frac{40}{2} = 20$$ $$x_2 = \frac{-6 - 46}{2} = \frac{-52}{2} = -26$$ 11. **Find corresponding length and width for each $x$:** - For $x=20$: - Length = $20 + 8 = 28$ - Width = $20 - 2 = 18$ - For $x=-26$: - Length = $-26 + 8 = -18$ (not possible since length cannot be negative) - Width = $-26 - 2 = -28$ (not possible) 12. **Conclusion:** The valid dimensions are length = 28 yards and width = 18 yards. **Final answer:** Length = 28, Width = 18 This corresponds to option c) 18 and 28 (width and length respectively).