what is the perimeter of rhombus abcd?

10 units
20 units
2\sqrt{7} units
4\sqrt{7} units

Question

what is the perimeter of rhombus abcd?

10 units
20 units
2\sqrt{7} units
4\sqrt{7} 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": [ "Rhombus Perimeter" ], "current_concepts": [ "Distance Formula", "Rhombus Perimeter" ] } ## Calculate the length of one side of the rhombus $$ \begin{aligned} A &= (1, 1) \ D &= (-2, 5) \ AD &= \sqrt{(-2 - 1)^2 + (5 - 1)^2} \ AD &= \sqrt{(-3)^2 + 4^2} \ AD &= \sqrt{9 + 16} \ AD &= \sqrt{25} = 5 \end{aligned} $$ ## Calculate the perimeter of the rhombus $$ \begin{aligned} \text{Perimeter} &= 4 \times \text{side length} \ \text{Perimeter} &= 4 \times 5 = 20 \end{aligned} $$

10 units

20 units

2$\sqrt{7}$ units

4$\sqrt{7}$ units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the length of one side of the rhombus

Calculate the perimeter of the rhombus

Answer: