if the legs of an isosceles right triangle have a length of (15\sqrt{2}\) ft, what is the length of the hypotenuse?

7.5 feet
(15\sqrt{2}\) feet
(15\sqrt{3}\) feet
30 feet

Question

if the legs of an isosceles right triangle have a length of (15\sqrt{2}\) ft, what is the length of the hypotenuse?

7.5 feet
(15\sqrt{2}\) feet
(15\sqrt{3}\) feet
30 feet

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Isosceles Right Triangle Properties", "Pythagorean Theorem" ], "new_concepts": [], "current_concepts": [ "Isosceles Right Triangle Properties", "Pythagorean Theorem" ] } ## Identify the given values and formula $$ \begin{aligned} &\text{Leg length } (a) = 15\sqrt{2}\text{ ft}\ &\text{Hypotenuse } (c) = a\sqrt{2} \end{aligned} $$ ## Calculate the hypotenuse length $$ \begin{aligned} c &= (15\sqrt{2}) \cdot \sqrt{2} \ c &= 15 \cdot 2 \ c &= 30\text{ feet} \end{aligned} $$

(A) 7.5 feet

(B) $15\sqrt{2}$ feet

(C) $15\sqrt{3}$ feet

(D) 30 feet

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Isosceles Right Triangle Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Calculate the hypotenuse length

Answer: