{"@context":"https://schema.org/","@type":"Quiz","name":"

Which equation shows the relationship between the side lengths of the given triangle?

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","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-71"}],"about":{"@type":"Thing","name":"Math, Geometry and Trigonometry, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Geometry and Trigonometry","Duplicate"],"name":"

Which equation shows the relationship between the side lengths of the given triangle?

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","comment":{"@type":"Comment","text":"

Choice C is correct. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Therefore, $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. For the given right triangle, the lengths of the legs are 4 and $b$, and the length of the hypotenuse is 19. Substituting 4 for $a$ and 19 for $c$ in the equation $a^{2}+b^{2}=c^{2}$ yields $4^{2}+b^{2}=19^{2}$. Thus, the relationship between the side lengths of the given triangle is $4^{2}+b^{2}=19^{2}$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

"},"encodingFormat":"text/markdown","text":"

Which equation shows the relationship between the side lengths of the given triangle?

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","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$4b=19$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$4+b=19$

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$4^{2}-b^{2}=19^{2}$

"}],"acceptedAnswer":{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$4^{2}+b^{2}=19^{2}$

","comment":{"@type":"Comment","text":"

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"}}},"url":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-71"}