the perimeter of a square is 56 cm. what is the approximate length of its diagonal?

10.6 cm
14.0 cm
15.0 cm
19.8 cm

Question

the perimeter of a square is 56 cm. what is the approximate length of its diagonal?

10.6 cm
14.0 cm
15.0 cm
19.8 cm

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Square Properties", "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Square Properties", "Pythagorean Theorem", "Special Right Triangles" ] } ## Find the side length of the square $$ \begin{aligned} P &= 56\text{ cm} \ s &= \frac{P}{4} = \frac{56}{4} = 14\text{ cm} \end{aligned} $$ ## Calculate the length of the diagonal $$ \begin{aligned} d &= s\sqrt{2} \ d &= 14\sqrt{2} \approx 14 \times 1.4142 \approx 19.799\text{ cm} \end{aligned} $$ ## Match with the closest option $$ d \approx 19.8\text{ cm} $$

(A) 10.6 cm

(B) 14.0 cm

(C) 15.0 cm

(D) 19.8 cm

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

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QUESTION IMAGE

Question

Explanation:

Find the side length of the square

Calculate the length of the diagonal

Match with the closest option

Answer: