Question

1. 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.

Explanation:

Step1: Find side length of square

Let side length of square be \( s \). Area of square \( A = s^2 = 75 \), so \( s=\sqrt{75}\approx8.66 \) ft.

Step2: Calculate perimeter of square

Perimeter of square \( P = 4s \). Substitute \( s\approx8.66 \), we get \( P = 4\times8.66 = 34.64 \) ft.

Step3: Compare with 32 ft

Since \( 34.64>32 \), the material is not enough.

Answer:

Tristan does not have enough material. The side length of the square garden with area 75 \( \text{ft}^2 \) is \( \sqrt{75}\approx8.66 \) ft, so the perimeter is \( 4\times8.66 = 34.64 \) ft, which is greater than 32 ft.