which sets of side lengths represent pythagorean triples? check all that apply.

1, 2, 5
6, 8, 14
8, 15, 17
10, 24, 26
15, 20, 30
28, 45, 53

Question

which sets of side lengths represent pythagorean triples? check all that apply.

1, 2, 5
  6, 8, 14
  8, 15, 17
  10, 24, 26
  15, 20, 30
  28, 45, 53

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem", "Pythagorean Triples" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Pythagorean Triples" ] } ## Check the definition of a Pythagorean triple $$ a^2 + b^2 = c^2 \quad \text{where } a, b, c \in \mathbb{Z}^+ \text{ and } a \le b < c $$ ## Evaluate each given set of side lengths $$ \begin{aligned} &\text{Set 1: } 1, 2, 5 \implies 1^2 + 2^2 = 1 + 4 = 5 e 5^2 \quad (\text{False}) \ &\text{Set 2: } 6, 8, 14 \implies 6^2 + 8^2 = 36 + 64 = 100 e 14^2 \quad (\text{False}) \ &\text{Set 3: } 8, 15, 17 \implies 8^2 + 15^2 = 64 + 225 = 289 = 17^2 \quad (\text{True}) \ &\text{Set 4: } 10, 24, 26 \implies 10^2 + 24^2 = 100 + 576 = 676 = 26^2 \quad (\text{True}) \ &\text{Set 5: } 15, 20, 30 \implies 15^2 + 20^2 = 225 + 400 = 625 e 30^2 \quad (\text{False}) \ &\text{Set 6: } 28, 45, 53 \implies 28^2 + 45^2 = 784 + 2025 = 2809 = 53^2 \quad (\text{True}) \end{aligned} $$ ## Identify the correct sets $$ \{8, 15, 17\}, \quad \{10, 24, 26\}, \quad \{28, 45, 53\} $$

1, 2, 5

6, 8, 14

8, 15, 17

10, 24, 26

15, 20, 30

28, 45, 53

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Pythagorean Triples" ] }

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QUESTION IMAGE

Question

Explanation:

Check the definition of a Pythagorean triple

Evaluate each given set of side lengths

Identify the correct sets

Answer: