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", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Properties of Rectangles", "Pythagorean Theorem", "Perimeter in Coordinate Plane" ], "new_concepts": [], "current_concepts": [ "Properties of Rectangles", "Pythagorean Theorem", "Perimeter in Coordinate Plane" ] } ## Identify given dimensions Using the *Properties of Rectangles* knowledge point $$ \begin{aligned} &\text{Rectangle } WXYZ \text{ has opposite sides of equal length.}\ &ZY = WX = 2\sqrt{10} \end{aligned} $$ ## Calculate remaining side lengths Using the *Pythagorean Theorem* and *Perimeter in Coordinate Plane* knowledge points $$ \begin{aligned} &W = (-6, 6),\quad Z = (-9, 5)\ &WZ = \sqrt{(-6 - (-9))^2 + (6 - 5)^2} = \sqrt{3^2 + 1^2} = \sqrt{10}\ &XY = WZ = \sqrt{10} \end{aligned} $$ ## Compute the total perimeter Using the *Perimeter in Coordinate Plane* knowledge point $$ \begin{aligned} P &= WX + XY + YZ + ZW\ P &= 2\sqrt{10} + \sqrt{10} + 2\sqrt{10} + \sqrt{10}\ P &= 6\sqrt{10} \end{aligned} $$

(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 in Coordinate Plane" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given dimensions

Calculate remaining side lengths

Compute the total perimeter

Answer: