which of these four sets of side lengths will form a right triangle?

set 1: 10 cm, 26 cm, 24 cm
set 2: 4 in., 2 in., 6 in.
set 3: 14 mm, 13 mm, 15 mm
set 4: 10 ft, 30 ft, 20 ft

- set 1
- set 2
- set 3
- set 4

Question

which of these four sets of side lengths will form a right triangle?

set 1: 10 cm, 26 cm, 24 cm
set 2: 4 in., 2 in., 6 in.
set 3: 14 mm, 13 mm, 15 mm
set 4: 10 ft, 30 ft, 20 ft

- set 1
- set 2
- set 3
- set 4

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", "Triangle Inequality Theorem" ] } ## Check the triangle inequality and Pythagorean relation for each set $$ \begin{aligned} &\text{Set 1: } 10, 24, 26 \ &10 + 24 = 34 > 26 \quad (\text{Valid triangle}) \ &10^2 + 24^2 = 100 + 576 = 676 \ &26^2 = 676 \ &10^2 + 24^2 = 26^2 \quad (\text{Right triangle}) \end{aligned} $$ ## Verify remaining sets to confirm uniqueness $$ \begin{aligned} &\text{Set 2: } 2, 4, 6 \implies 2 + 4 = 6 \quad (\text{Not a triangle}) \ &\text{Set 3: } 13, 14, 15 \implies 13^2 + 14^2 = 169 + 196 = 365 e 15^2 \quad (\text{Not a right triangle}) \ &\text{Set 4: } 10, 20, 30 \implies 10 + 20 = 30 \quad (\text{Not a triangle}) \end{aligned} $$ ## Identify the correct option $$ \text{Set 1 forms a right triangle.} $$

Set 1

Set 2

Set 3

Set 4

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

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QUESTION IMAGE

Question

Explanation:

Check the triangle inequality and Pythagorean relation for each set

Verify remaining sets to confirm uniqueness

Identify the correct option

Answer: