how much longer is the hypotenuse of the triangle than its shorter leg?

(2\text{ ft})
(4\text{ ft})
(8\text{ ft})
(10\text{ ft})

Question

how much longer is the hypotenuse of the triangle than its shorter leg?

(2\text{ ft})
(4\text{ ft})
(8\text{ ft})
(10\text{ 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", "Right Triangle Properties" ] } ## Calculate the hypotenuse using the Pythagorean theorem $$ \begin{aligned} c^2 &= a^2 + b^2 \ c^2 &= 6^2 + 8^2 \ c^2 &= 36 + 64 \ c^2 &= 100 \ c &= 10\text{ ft} \end{aligned} $$ ## Identify the shorter leg of the right triangle $$ \begin{aligned} \text{Leg 1} &= 6\text{ ft} \ \text{Leg 2} &= 8\text{ ft} \ \text{Shorter leg} &= 6\text{ ft} \end{aligned} $$ ## Calculate the difference between the hypotenuse and the shorter leg $$ \begin{aligned} \text{Difference} &= \text{Hypotenuse} - \text{Shorter leg} \ \text{Difference} &= 10\text{ ft} - 6\text{ ft} \ \text{Difference} &= 4\text{ ft} \end{aligned} $$

(A) 2 ft

(B) 4 ft

(C) 8 ft

(D) 10 ft

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

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QUESTION IMAGE

Question

Explanation:

Calculate the hypotenuse using the Pythagorean theorem

Identify the shorter leg of the right triangle

Calculate the difference between the hypotenuse and the shorter leg

Answer: