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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula" ], "new_concepts": [ "Perimeter of a Rectangle" ], "current_concepts": [ "Distance Formula", "Perimeter of a Rectangle" ] } ## 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 $$ \begin{aligned} \text{Perimeter} &= 2(WZ + WX) \ &= 2(\sqrt{10} + 2\sqrt{10}) \ &= 2(3\sqrt{10}) \ &= 6\sqrt{10} \end{aligned} $$

(A) $\sqrt{10}$ units

(B) $2\sqrt{10}$ units

(C) $6\sqrt{10}$ units

(D) $8\sqrt{10}$ units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perimeter of a Rectangle" ] }

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Question

Explanation:

Calculate the length of side WZ

Calculate the perimeter of rectangle WXYZ

Answer: