what is z in the figure shown?

a $z = \sqrt{x^2 + y^2}$
b $z = x + y$
c $z = (x + y)^2$
d $z = \sqrt{x + y}$

if b is your answer, click the next button. otherwise, select another answer.

Question

what is z in the figure shown?

a $z = \sqrt{x^2 + y^2}$
b $z = x + y$
c $z = (x + y)^2$
d $z = \sqrt{x + y}$

if b is your answer, click the next button. otherwise, select another answer.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Pythagorean Theorem" ], "current_concepts": [ "Pythagorean Theorem", "Right Triangles" ] } ## Identify the given geometric properties The figure shows a right-angled triangle with legs of length $x$ and $y$, and a hypotenuse of length $z$. ## Apply the Pythagorean theorem $$ z^2 = x^2 + y^2 $$ ## Solve for the hypotenuse z $$ z = \sqrt{x^2 + y^2} $$

(A) $z = \sqrt{x^2 + y^2}$

(B) $z = x + y$

(C) $z = (x + y)^2$

(D) $z = \sqrt{x + y}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric properties

Apply the Pythagorean theorem

Solve for the hypotenuse z

Answer: