question 3 of 5

select the correct answer.

what is the perimeter of rectangle mnop, rounded to the nearest tenth of a meter?

79.2 m
88.1 m
67.6 m
76.5 m

Question

question 3 of 5

select the correct answer.

what is the perimeter of rectangle mnop, rounded to the nearest tenth of a meter?

79.2 m
88.1 m
67.6 m
76.5 m

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": [ "Special Right Triangles" ], "new_concepts": [ "Perimeter of a Rectangle" ], "current_concepts": [ "Special Right Triangles", "Perimeter of a Rectangle" ] } ## Identify the properties of the triangle Using the *Special Right Triangles* knowledge point $$ \begin{aligned} &\triangle MNO \text{ is a } 30^\circ\text{-}60^\circ\text{-}90^\circ \text{ right triangle.}\ &MO = 28\text{ m (hypotenuse)} \end{aligned} $$ ## Calculate the side lengths of the rectangle Using the *Special Right Triangles* knowledge point $$ \begin{aligned} &MN = \frac{MO}{2} = \frac{28}{2} = 14\text{ m}\ &NO = MN \cdot \sqrt{3} = 14\sqrt{3}\text{ m} \end{aligned} $$ ## Calculate the perimeter of the rectangle We find the perimeter of rectangle $MNOP$: $$ \begin{aligned} P &= 2(MN + NO)\ P &= 2(14 + 14\sqrt{3})\ P &= 28 + 28\sqrt{3}\ P &\approx 28 + 28(1.73205)\ P &\approx 28 + 48.497\ P &\approx 76.497\text{ m} \end{aligned} $$ ## Round to the nearest tenth We round the calculated perimeter to the nearest tenth of a meter: $$ P \approx 76.5\text{ m} $$

(A) 79.2 m

(B) 88.1 m

(C) 67.6 m

(D) 76.5 m

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Special Right Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the properties of the triangle

Calculate the side lengths of the rectangle

Calculate the perimeter of the rectangle

Round to the nearest tenth

Answer: