A Square Garden Plot Has An Area Of $75 \, \text{ft}^2$. Find The Length Of Each Side In Simplest Radical Form. Calculate The Length Of Each Side To The Nearest Tenth Of A Foot.A. $\frac{75}{4}; \, 18.8 \, \text{ft}$B. $5

Introduction

In this article, we will explore the concept of finding the length of each side of a square garden plot given its area. We will use the formula for the area of a square, which is side squared, to find the length of each side in simplest radical form. Additionally, we will calculate the length of each side to the nearest tenth of a foot.

The Formula for the Area of a Square

The formula for the area of a square is given by:

$$A = s^2$$

where $A$ is the area of the square and $s$ is the length of each side.

Given Information

We are given that the area of the square garden plot is $75 \, \text{ft}^2$. We can use this information to find the length of each side.

Finding the Length of Each Side

To find the length of each side, we can rearrange the formula for the area of a square to solve for $s$:

$$s = \sqrt{A}$$

Substituting the given value of $A$, we get:

$$s = \sqrt{75}$$

To simplify the radical, we can factor the number under the square root sign:

$$s = \sqrt{25 \cdot 3}$$

Using the property of radicals that allows us to separate the square root of a product into the product of the square roots, we get:

$$s = \sqrt{25} \cdot \sqrt{3}$$

Since $\sqrt{25} = 5$, we can simplify the expression further:

$$s = 5\sqrt{3}$$

Calculating the Length of Each Side to the Nearest Tenth of a Foot

To calculate the length of each side to the nearest tenth of a foot, we can use a calculator to evaluate the expression $5\sqrt{3}$:

$$5\sqrt{3} \approx 8.660254037844386$$

Rounding this value to the nearest tenth of a foot, we get:

$$s \approx 8.6 \, \text{ft}$$

Conclusion

In this article, we found the length of each side of a square garden plot given its area. We used the formula for the area of a square to find the length of each side in simplest radical form and calculated the length of each side to the nearest tenth of a foot.

Comparison with Given Options

Let's compare our result with the given options:

A. $\frac{75}{4}; \, 18.8 \, \text{ft}$

B. $5\sqrt{3}; \, 8.6 \, \text{ft}$

Our result matches option B.

Final Answer

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Introduction

In our previous article, we explored the concept of finding the length of each side of a square garden plot given its area. We used the formula for the area of a square to find the length of each side in simplest radical form and calculated the length of each side to the nearest tenth of a foot. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What is the formula for the area of a square?

A: The formula for the area of a square is given by:

$$A = s^2$$

where $A$ is the area of the square and $s$ is the length of each side.

Q: How do I find the length of each side of a square given its area?

A: To find the length of each side, you can rearrange the formula for the area of a square to solve for $s$:

$$s = \sqrt{A}$$

Q: What if the area of the square is not a perfect square?

A: If the area of the square is not a perfect square, you will need to simplify the radical expression. For example, if the area is $75 \, \text{ft}^2$, you can factor the number under the square root sign:

$$s = \sqrt{75} = \sqrt{25 \cdot 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3}$$

Q: How do I calculate the length of each side to the nearest tenth of a foot?

A: To calculate the length of each side to the nearest tenth of a foot, you can use a calculator to evaluate the expression $s = \sqrt{A}$ and then round the result to the nearest tenth of a foot.

Q: What if I get a different answer than the one given in the article?

A: If you get a different answer than the one given in the article, it may be due to a calculation error or a misunderstanding of the problem. Double-check your work and make sure you are using the correct formula and values.

Q: Can I use this method to find the length of each side of a rectangle?

A: No, this method is only applicable to squares. If you need to find the length of each side of a rectangle, you will need to use a different method.

Q: What if the area of the square is negative?

A: The area of a square cannot be negative, so if you are given a negative area, it is likely an error.

Q: Can I use this method to find the area of a square given the length of each side?

A: Yes, you can use this method to find the area of a square given the length of each side. Simply square the length of each side to find the area:

$$A = s^2$$

Conclusion

In this article, we answered some frequently asked questions related to finding the length of each side of a square given its area. We hope this article has been helpful in clarifying any confusion and providing additional guidance on this topic.

Additional Resources

For more information on this topic, you may want to consult the following resources:

• [Your website or online resource]
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Final Answer

The final answer is $\boxed{5\sqrt{3}}$.