Question: 5. Tristan wants to build a square garden in his backyard that will cover an area of 75 ft². If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain.
1. **State the problem:** Tristan wants to build a square garden with an area of $$75\text{ ft}^2$$ and has $$32$$ feet of material for the perimeter. We need to check if $$32$$ feet is enough for the perimeter.
2. **Recall formulas:**
- Area of a square: $$A = s^2$$ where $$s$$ is the side length.
- Perimeter of a square: $$P = 4s$$.
3. **Find the side length from the area:**
$$s = \sqrt{A} = \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3} \approx 8.66$$ feet.
4. **Calculate the perimeter needed:**
$$P = 4s = 4 \times 8.66 = 34.64$$ feet.
5. **Compare with available material:**
Tristan has $$32$$ feet, but the garden needs approximately $$34.64$$ feet.
6. **Conclusion:**
Tristan does **not** have enough material because $$32 < 34.64$$ feet.
Therefore, Tristan cannot build the garden with the given material.