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1. A square garden plot has an area of [tex]$24 \, \text{ft}^2$[/tex].

a. Find the length of each side in simplest radical form.

b. Calculate the length of each side to the nearest tenth of a foot.

A. [tex]2 \sqrt{6} \, \text{ft} ; 4.9 \, \text{ft}[/tex]

B. [tex]\frac{24}{4} \, \text{ft} ; 6 \, \text{ft}[/tex]

C. [tex]\sqrt{24} \, \text{ft} ; 5 \, \text{ft}[/tex]

D. [tex]\frac{\sqrt{24}}{2} \, \text{ft} ; 2.45 \, \text{ft}[/tex]

Sagot :

GinnyAnswer
Sure, let's solve the problem step by step:

### Part (a): Find the length of each side in simplest radical form.

1. Understand the problem: We are given the area of a square garden plot, which is [tex]\( 24 \text{ ft}^2 \)[/tex]. We need to determine the length of each side in simplest radical form.

2. Formula: The area of a square is given by [tex]\( \text{Area} = \text{side}^2 \)[/tex].

3. Set up the equation: Let [tex]\( s \)[/tex] be the length of a side of the square. We have:
[tex]\[ s^2 = 24 \][/tex]

4. Solve for [tex]\( s \)[/tex]: Take the square root of both sides:
[tex]\[ s = \sqrt{24} \][/tex]

5. Simplify the radical: To express [tex]\( \sqrt{24} \)[/tex] in simplest radical form, note that:
[tex]\[ 24 = 4 \times 6 \implies \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \][/tex]

So, the length of each side in simplest radical form is:
[tex]\[ s = 2\sqrt{6} \text{ feet} \][/tex]

### Part (b): Calculate the length of each side to the nearest tenth of a foot.

1. Use the simplified radical form: We found that [tex]\( s = 2\sqrt{6} \)[/tex].

2. Approximate the value numerically: Calculate [tex]\( 2\sqrt{6} \)[/tex]. Typically, the calculator or approximation of [tex]\( \sqrt{6} \approx 2.449 \)[/tex]:
[tex]\[ 2 \times 2.449 = 4.898 \][/tex]

3. Round to the nearest tenth: The value [tex]\( 4.898 \)[/tex] rounded to the nearest tenth is:
[tex]\[ 4.9 \text{ feet} \][/tex]

### Summary of the Results
- The length of each side in simplest radical form is [tex]\( 2\sqrt{6} \)[/tex] feet.
- The length of each side rounded to the nearest tenth of a foot is [tex]\( 4.9 \)[/tex] feet.

Given the multiple-choice options, the correct one is:

[tex]\[ 2\sqrt{6} ; 4.9 \text{ ft} \][/tex]
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