what is the perimeter of kite wxyz?

$2\sqrt{53} + 2$ units
$2\sqrt{53} + 5$ units
$2\sqrt{53} + 10$ units
$2\sqrt{53} + 14$ units

Question

what is the perimeter of kite wxyz?

$2\sqrt{53} + 2$ units
$2\sqrt{53} + 5$ units
$2\sqrt{53} + 10$ units
$2\sqrt{53} + 14$ units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Kite Definition", "Distance Formula" ], "new_concepts": [], "current_concepts": [ "Kite Definition", "Distance Formula", "Perimeter of Polygons" ] } ## Calculate the lengths of the shorter adjacent sides $$ \begin{aligned} &W = (-3, 3), \quad X = (2, 3), \quad Z = (-3, -2)\ &WX = \sqrt{(2 - (-3))^2 + (3 - 3)^2} = \sqrt{5^2 + 0^2} = 5\ &WZ = \sqrt{(-3 - (-3))^2 + (-2 - 3)^2} = \sqrt{0^2 + (-5)^2} = 5 \end{aligned} $$ ## Calculate the lengths of the longer adjacent sides $$ \begin{aligned} &X = (2, 3), \quad Y = (4, -4), \quad Z = (-3, -2)\ &XY = \sqrt{(4 - 2)^2 + (-4 - 3)^2} = \sqrt{2^2 + (-7)^2} = \sqrt{4 + 49} = \sqrt{53}\ &ZY = \sqrt{(4 - (-3))^2 + (-4 - (-2))^2} = \sqrt{7^2 + (-2)^2} = \sqrt{49 + 4} = \sqrt{53} \end{aligned} $$ ## Sum the side lengths to find the perimeter $$ \text{Perimeter} = WX + WZ + XY + ZY = 5 + 5 + \sqrt{53} + \sqrt{53} = 2\sqrt{53} + 10 $$

(A) $2\sqrt{53} + 2$ units

(B) $2\sqrt{53} + 5$ units

(C) $2\sqrt{53} + 10$ units

(D) $2\sqrt{53} + 14$ units

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

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QUESTION IMAGE

Question

Explanation:

Calculate the lengths of the shorter adjacent sides

Calculate the lengths of the longer adjacent sides

Sum the side lengths to find the perimeter

Answer: