Sure! To create a square model for a garden with an area of [tex]\(32 \, \text{square feet}\)[/tex], let's proceed step-by-step:
1. Understanding the Shape:
- We know that a square has four equal sides.
- The area of a square is calculated by squaring the length of one of its sides.
2. Given Information:
- The area of the garden is [tex]\(32 \, \text{square feet}\)[/tex].
3. Calculating the Side Length:
- Let's denote the side length of the square as [tex]\(s\)[/tex].
- The formula to find the area of a square is [tex]\(s^2 = \text{area}\)[/tex].
- Since the area is [tex]\(32 \, \text{square feet}\)[/tex], we can set up the equation [tex]\(s^2 = 32\)[/tex].
4. Solving for [tex]\(s\)[/tex]:
- To find the side length [tex]\(s\)[/tex], we take the square root of [tex]\(32\)[/tex]:
[tex]\[
s = \sqrt{32}
\][/tex]
- The calculation gives us:
[tex]\[
s \approx 5.656854249492381 \, \text{feet}
\][/tex]
5. Conclusion:
- The side length of the square model representing the garden is approximately [tex]\(5.656854249492381 \, \text{feet}\)[/tex].
- Therefore, if we construct a square with each side measuring about [tex]\(5.656854249492381 \, \text{feet}\)[/tex], it will have an area of [tex]\(32 \, \text{square feet}\)[/tex].
This model effectively represents the given area using a square shape.
