Question

ricardo has a square hot tub. he wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5.

if the pool is to be 24 ft on each side, what is the length of one side of the hot tub?

4 ft
4.8 ft
6 ft
7.2 ft

Explanation:

<pre_analysis>
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"concepts_used": [
"Geometric Dilation"
],
"new_concepts": [],
"current_concepts": [
"Geometric Dilation",
"Scale Factor"
]
}
</pre_analysis>

<reasoning>

Identify the dilation formula

\[
\text{Side of Pool} = \text{Scale Factor} \times \text{Side of Hot Tub}
\]

Substitute the given values

\[
24 = 5 \times x
\]

Solve for the unknown side length

\[
x = \frac{24}{5} = 4.8\text{ ft}
\]
</reasoning>

<answer>
<mcq-option>(A) 4 ft</mcq-option>
<mcq-correct>(B) 4.8 ft</mcq-correct>
<mcq-option>(C) 6 ft</mcq-option>
<mcq-option>(D) 7.2 ft</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Dilation"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
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"step_cot",
"multiple_choice_formatter",
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],
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"concepts_used": [
"Geometric Dilation"
],
"new_concepts": [],
"current_concepts": [
"Geometric Dilation",
"Scale Factor"
]
}
</pre_analysis>

<reasoning>

Identify the dilation formula

\[
\text{Side of Pool} = \text{Scale Factor} \times \text{Side of Hot Tub}
\]

Substitute the given values

\[
24 = 5 \times x
\]

Solve for the unknown side length

\[
x = \frac{24}{5} = 4.8\text{ ft}
\]
</reasoning>

<answer>
<mcq-option>(A) 4 ft</mcq-option>
<mcq-correct>(B) 4.8 ft</mcq-correct>
<mcq-option>(C) 6 ft</mcq-option>
<mcq-option>(D) 7.2 ft</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Geometric Dilation"
]
}
</post_analysis>