what is the perimeter of rhombus lmno?

20 units
24 units
40 units
48 units

Question

what is the perimeter of rhombus lmno?

20 units
24 units
40 units
48 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Properties of Quadrilaterals" ], "new_concepts": [ "Rhombus Properties" ], "current_concepts": [ "Properties of Quadrilaterals", "Rhombus Properties" ] } ## Equate the side lengths of the rhombus $$ \begin{aligned} LM &= MN \ 3x - 3 &= x + 7 \end{aligned} $$ ## Solve for x $$ \begin{aligned} 2x &= 10 \ x &= 5 \end{aligned} $$ ## Calculate the side length and perimeter $$ \begin{aligned} \text{Side length} &= 5 + 7 = 12 \ \text{Perimeter} &= 4 \times 12 = 48 \end{aligned} $$

(A) 20 units

(B) 24 units

(C) 40 units

(D) 48 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Rhombus Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Equate the side lengths of the rhombus

Solve for x

Calculate the side length and perimeter

Answer: