which best explains why this triangle is or is not a right triangle?

this triangle is not a right triangle: (39^2 + 15^2 \
eq 36^2).
this triangle is not a right triangle: (39^2 + 36^2 \
eq 15^2).
this triangle is a right triangle: (36^2 + 39^2 = 15^2).
this triangle is a right triangle: (36^2 + 15^2 = 39^2).

Question

which best explains why this triangle is or is not a right triangle?

this triangle is not a right triangle: (39^2 + 15^2 \
eq 36^2).
this triangle is not a right triangle: (39^2 + 36^2 \
eq 15^2).
this triangle is a right triangle: (36^2 + 39^2 = 15^2).
this triangle is a right triangle: (36^2 + 15^2 = 39^2).

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" ], "new_concepts": [], "current_concepts": [ "Pythagorean Theorem", "Pythagorean Triples" ] } ## Identify the side lengths and hypotenuse candidate $$ \begin{aligned} &a = 15\ &b = 36\ &c = 39 \quad (\text{longest side}) \end{aligned} $$ ## Apply the Pythagorean theorem converse $$ \begin{aligned} &a^2 + b^2 = 15^2 + 36^2 = 225 + 1296 = 1521\ &c^2 = 39^2 = 1521\ &15^2 + 36^2 = 39^2 \quad (1521 = 1521) \end{aligned} $$ ## Match with the correct option $$ 36^2 + 15^2 = 39^2 \implies \text{This triangle is a right triangle.} $$

This triangle is not a right triangle: $39^2 + 15^2 eq 36^2$.

This triangle is not a right triangle: $39^2 + 36^2 eq 15^2$.

This triangle is a right triangle: $36^2 + 39^2 = 15^2$.

This triangle is a right triangle: $36^2 + 15^2 = 39^2$.

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the side lengths and hypotenuse candidate

Apply the Pythagorean theorem converse

Match with the correct option

Answer: