which set of side lengths forms a right triangle?

2, 3, 13
4, 6, 10
9, 12, 18
15, 36, 39

Question

which set of side lengths forms a right triangle?

2, 3, 13
4, 6, 10
9, 12, 18
15, 36, 39

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" ] } ## State the condition for a right triangle $$ a^2 + b^2 = c^2 \quad (\text{where } c \text{ is the longest side}) $$ ## Test each set of side lengths $$ \begin{aligned} &\text{Option 1: } 2, 3, 13 \implies 2 + 3 = 5 < 13 \quad (\text{not a triangle})\ &\text{Option 2: } 4, 6, 10 \implies 4 + 6 = 10 \quad (\text{not a triangle})\ &\text{Option 3: } 9, 12, 18 \implies 9^2 + 12^2 = 81 + 144 = 225 e 18^2 \quad (324)\ &\text{Option 4: } 15, 36, 39 \implies 15^2 + 36^2 = 225 + 1296 = 1521 = 39^2 \quad (1521) \end{aligned} $$ ## Identify the correct right triangle $$ 15^2 + 36^2 = 39^2 $$

(A) 2, 3, 13

(B) 4, 6, 10

(C) 9, 12, 18

(D) 15, 36, 39

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

State the condition for a right triangle

Test each set of side lengths

Identify the correct right triangle

Answer: