question 18 of 40

a triangle with sides of lengths 10, 18, and 21 is a right triangle.

a. true
b. false

Question

question 18 of 40

a triangle with sides of lengths 10, 18, and 21 is a right triangle.

a. true
b. false

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 in Circles" ], "new_concepts": [ "Pythagorean Theorem Converse" ], "current_concepts": [ "Pythagorean Theorem Converse", "Right Triangle Definition" ] } ## Identify the side lengths and the hypotenuse candidate $$ \begin{aligned} &a = 10 \ &b = 18 \ &c = 21 \end{aligned} $$ ## Apply the Pythagorean Theorem converse $$ \begin{aligned} &a^2 + b^2 = 10^2 + 18^2 = 100 + 324 = 424 \ &c^2 = 21^2 = 441 \end{aligned} $$ ## Compare the sum of squares to the square of the longest side $$ \begin{aligned} &424 eq 441 \ &a^2 + b^2 eq c^2 \end{aligned} $$

A. True

B. False

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the side lengths and the hypotenuse candidate

Apply the Pythagorean Theorem converse

Compare the sum of squares to the square of the longest side

Answer: