Tristan wants to build a square garden in his backyard that will cover an area of 75ft^(2). If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain.
The correct answer and explanation is:
To determine if Tristan has enough material for the perimeter of his square garden, we need to first calculate the dimensions of the garden and then determine if 32 feet of material will be sufficient for the perimeter.
Step 1: Determine the Side Length of the Garden
Since the garden is square-shaped, we know that the area AA of a square is calculated using the formula: A=side length2A = \text{side length}^2
We are told that the area of the garden is 75 square feet: 75=side length275 = \text{side length}^2
To find the side length, take the square root of both sides: side length=75≈8.66 feet\text{side length} = \sqrt{75} \approx 8.66 \, \text{feet}
Step 2: Calculate the Perimeter of the Garden
The perimeter PP of a square is calculated by multiplying the side length by 4 (since all four sides are equal): P=4×side length=4×8.66≈34.64 feetP = 4 \times \text{side length} = 4 \times 8.66 \approx 34.64 \, \text{feet}
Step 3: Compare Available Material to Required Perimeter
Tristan has 32 feet of material for the perimeter. However, the required perimeter of the garden is approximately 34.64 feet. Since 34.64 feet is more than the 32 feet of material Tristan has, he does not have enough material to cover the perimeter.
Conclusion:
Tristan needs about 34.64 feet of material to construct the perimeter of his square garden, but he only has 32 feet of material. Therefore, he does not have enough material to complete the project. Tristan will need to obtain approximately 2.64 more feet of material to ensure the perimeter is fully covered.