what is the length of the hypotenuse of the triangle?

26 ft
34 ft
68 ft
74 ft

Question

what is the length of the hypotenuse of the triangle?

26 ft
34 ft
68 ft
74 ft

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" ] } ## Identify the given side lengths of the right triangle $$ \begin{aligned} a &= 10\text{ ft} \ b &= 24\text{ ft} \end{aligned} $$ ## Apply the Pythagorean theorem to find the hypotenuse $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 10^2 + 24^2 \ c^2 &= 100 + 576 \ c^2 &= 676 \end{aligned} $$ ## Solve for the hypotenuse length $$ \begin{aligned} c &= \sqrt{676} \ c &= 26\text{ ft} \end{aligned} $$

(A) 26 ft

(B) 34 ft

(C) 68 ft

(D) 74 ft

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

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QUESTION IMAGE

Question

Explanation:

Identify the given side lengths of the right triangle

Apply the Pythagorean theorem to find the hypotenuse

Solve for the hypotenuse length

Answer: