Question

in the diagram, \\(wz = \sqrt{26}\\).

what is the perimeter of parallelogram \\(wxyz\\)?

\\(2\sqrt{26} + 2\\) units
\\(2\sqrt{26} + 4\\) units
\\(2\sqrt{26} + 6\\) units
\\(2\sqrt{26} + 8\\) units

Explanation:

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<reasoning>

Identify given side lengths

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &WZ = \sqrt{26}\\ &XY = WZ = \sqrt{26} \end{aligned}$$

\]

Calculate horizontal side lengths

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &WX = 2 - (-2) = 4\\ &ZY = 1 - (-3) = 4\\ &WX = ZY = 4 \end{aligned}$$

\]

Compute the perimeter

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} P &= WX + XY + ZY + WZ\\ P &= 4 + \sqrt{26} + 4 + \sqrt{26}\\ P &= 2\sqrt{26} + 8 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(2\sqrt{26} + 2\) units</mcq-option>
<mcq-option>(B) \(2\sqrt{26} + 4\) units</mcq-option>
<mcq-option>(C) \(2\sqrt{26} + 6\) units</mcq-option>
<mcq-correct>(D) \(2\sqrt{26} + 8\) units</mcq-correct>
</answer>

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Answer:

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<reasoning>

Identify given side lengths

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &WZ = \sqrt{26}\\ &XY = WZ = \sqrt{26} \end{aligned}$$

\]

Calculate horizontal side lengths

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &WX = 2 - (-2) = 4\\ &ZY = 1 - (-3) = 4\\ &WX = ZY = 4 \end{aligned}$$

\]

Compute the perimeter

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} P &= WX + XY + ZY + WZ\\ P &= 4 + \sqrt{26} + 4 + \sqrt{26}\\ P &= 2\sqrt{26} + 8 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(2\sqrt{26} + 2\) units</mcq-option>
<mcq-option>(B) \(2\sqrt{26} + 4\) units</mcq-option>
<mcq-option>(C) \(2\sqrt{26} + 6\) units</mcq-option>
<mcq-correct>(D) \(2\sqrt{26} + 8\) units</mcq-correct>
</answer>

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