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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Properties of Parallelograms" ], "new_concepts": [ "Perimeter in Coordinate Plane" ], "current_concepts": [ "Properties of Parallelograms", "Perimeter in Coordinate Plane" ] } ## 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 $$ \begin{aligned} P &= WX + XY + ZY + WZ\ P &= 4 + \sqrt{26} + 4 + \sqrt{26}\ P &= 2\sqrt{26} + 8 \end{aligned} $$

(A) $2\sqrt{26} + 2$ units

(B) $2\sqrt{26} + 4$ units

(C) $2\sqrt{26} + 6$ units

(D) $2\sqrt{26} + 8$ units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Properties of Parallelograms" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given side lengths

Calculate horizontal side lengths

Compute the perimeter

Answer: