the length of side pq is choose an answer units.
the length of side qr is about choose an answer units.
the perimeter of the parallelogram pqrs is about choose an answer units.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Radicals", "Decimal Rounding" ], "new_concepts": [ "Distance Formula", "Perimeter of Parallelogram" ], "current_concepts": [ "Distance Formula", "Perimeter of Parallelogram", "Simplifying Radicals", "Decimal Rounding" ] } ## Identify coordinates of the vertices $$ P(-5, 3),\quad Q(-3, 3),\quad R(-4, 1),\quad S(-6, 1) $$ ## Calculate the lengths of the sides $$ \begin{aligned} &PQ = |-3 - (-5)| = 2\ &QR = \sqrt{(-4 - (-3))^2 + (1 - 3)^2} = \sqrt{(-1)^2 + (-2)^2} = \sqrt{5} \approx 2.24 \end{aligned} $$ ## Calculate the perimeter of the parallelogram $$ \text{Perimeter} = 2(PQ + QR) = 2(2 + \sqrt{5}) \approx 2(2 + 2.24) = 8.48 \approx 8.5 $$ The length of side PQ is 2 units. The length of side QR is about 2.2 units. The perimeter of the parallelogram PQRS is about 8.5 units. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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Question

Explanation:

Identify coordinates of the vertices

Calculate the lengths of the sides

Calculate the perimeter of the parallelogram

Answer: