Question

in the diagram, \\(zy = wx = 2\sqrt{10}\\). what is the perimeter of rectangle wxyz?

\\(\sqrt{10}\\) units
\\(2\sqrt{10}\\) units
\\(6\sqrt{10}\\) units
\\(8\sqrt{10}\\) units

Explanation:

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"new_concepts": [
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</pre_analysis>

<reasoning>

Calculate the length of side WZ

\[

$$\begin{aligned} WZ &= \sqrt{(-6 - (-9))^2 + (6 - 5)^2} \\ &= \sqrt{(3)^2 + (1)^2} \\ &= \sqrt{9 + 1} \\ &= \sqrt{10} \end{aligned}$$

\]

Calculate the perimeter of rectangle WXYZ

\[

$$\begin{aligned} \text{Perimeter} &= 2(WZ + WX) \\ &= 2(\sqrt{10} + 2\sqrt{10}) \\ &= 2(3\sqrt{10}) \\ &= 6\sqrt{10} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(\sqrt{10}\) units</mcq-option>
<mcq-option>(B) \(2\sqrt{10}\) units</mcq-option>
<mcq-correct>(C) \(6\sqrt{10}\) units</mcq-correct>
<mcq-option>(D) \(8\sqrt{10}\) units</mcq-option>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
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]
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Answer:

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"new_concepts": [
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</pre_analysis>

<reasoning>

Calculate the length of side WZ

\[

$$\begin{aligned} WZ &= \sqrt{(-6 - (-9))^2 + (6 - 5)^2} \\ &= \sqrt{(3)^2 + (1)^2} \\ &= \sqrt{9 + 1} \\ &= \sqrt{10} \end{aligned}$$

\]

Calculate the perimeter of rectangle WXYZ

\[

$$\begin{aligned} \text{Perimeter} &= 2(WZ + WX) \\ &= 2(\sqrt{10} + 2\sqrt{10}) \\ &= 2(3\sqrt{10}) \\ &= 6\sqrt{10} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(\sqrt{10}\) units</mcq-option>
<mcq-option>(B) \(2\sqrt{10}\) units</mcq-option>
<mcq-correct>(C) \(6\sqrt{10}\) units</mcq-correct>
<mcq-option>(D) \(8\sqrt{10}\) units</mcq-option>
</answer>

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