what is the length of the hypotenuse, $x$, if $(20, 21, x)$ is a pythagorean triple?

- 22
- 29
- 41
- 42

Question

what is the length of the hypotenuse, $x$, if $(20, 21, x)$ is a pythagorean triple?

- 22
- 29
- 41
- 42

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perfect Squares" ], "new_concepts": [ "Pythagorean Theorem", "Pythagorean Triples" ], "current_concepts": [ "Perfect Squares", "Pythagorean Theorem", "Pythagorean Triples" ] } ## Set up the Pythagorean equation $$ 20^2 + 21^2 = x^2 $$ ## Calculate the squares of the legs $$ \begin{aligned} 20^2 &= 400 \ 21^2 &= 441 \ x^2 &= 400 + 441 = 841 \end{aligned} $$ ## Solve for the hypotenuse x $$ \begin{aligned} x &= \sqrt{841} \ x &= 29 \end{aligned} $$

(A) 22

(B) 29

(C) 41

(D) 42

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

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QUESTION IMAGE

Question

Explanation:

Set up the Pythagorean equation

Calculate the squares of the legs

Solve for the hypotenuse x

Answer: