select the correct answer.

rounded to the nearest tenth, what is the perimeter of rectangle abcd?

- 48.3 cm
- 54.6 cm
- 60.0 cm
- 173.2 cm

Question

select the correct answer.

rounded to the nearest tenth, what is the perimeter of rectangle abcd?

- 48.3 cm
- 54.6 cm
- 60.0 cm
- 173.2 cm

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 Rectangles" ], "current_concepts": [ "Special Right Triangles", "Trigonometric Ratios", "Perimeter of Rectangles" ] } ## Identify the properties of the right triangle Using the *Special Right Triangles* knowledge point $$ \begin{aligned} &\triangle ACD \text{ is a } 30^\circ\text{-}60^\circ\text{-}90^\circ \text{ right triangle}\ &\text{Hypotenuse } AC = 20\text{ cm} \end{aligned} $$ ## Calculate the side lengths of the rectangle Using the *Special Right Triangles* knowledge point $$ \begin{aligned} &CD = \frac{AC}{2} = \frac{20}{2} = 10\text{ cm}\ &AD = CD \cdot \sqrt{3} = 10\sqrt{3}\text{ cm} \approx 17.3205\text{ cm} \end{aligned} $$ ## Calculate the perimeter of the rectangle Using the *Perimeter of Rectangles* knowledge point $$ \begin{aligned} &P = 2(AD + CD)\ &P = 2(10\sqrt{3} + 10) = 20\sqrt{3} + 20\ &P \approx 20(1.73205) + 20 = 34.641 + 20 = 54.641\text{ cm}\ &P \approx 54.6\text{ cm} \end{aligned} $$

(A) 48.3 cm

(B) 54.6 cm

(C) 60.0 cm

(D) 173.2 cm

{ "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 right triangle

Calculate the side lengths of the rectangle

Calculate the perimeter of the rectangle

Answer: