mrs. ibarra wants to create a right triangle for a geometry test. she plans to use 15, 36, and 41 as side lengths.

select the four true statements regarding the side lengths mrs. ibarra chose.

$15 + 36 41$, so the side lengths will form a triangle.
$15 + 36 = 41$, so those lengths will not form a triangle.
$15^2 + 36^2 = 1521$
$41^2 = 1681$
since $a^2 + b^2 \
eq c^2$, it will not be a right triangle.
$15^2 + 36^2 = 297$
$41^2 = 82$

Question

mrs. ibarra wants to create a right triangle for a geometry test. she plans to use 15, 36, and 41 as side lengths.

select the four true statements regarding the side lengths mrs. ibarra chose.

$15 + 36 > 41$, so the side lengths will form a triangle.
$15 + 36 = 41$, so those lengths will not form a triangle.
$15^2 + 36^2 = 1521$
$41^2 = 1681$
since $a^2 + b^2 \
eq c^2$, it will not be a right triangle.
$15^2 + 36^2 = 297$
$41^2 = 82$

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" ], "new_concepts": [ "Triangle Inequality Theorem" ], "current_concepts": [ "Pythagorean Theorem", "Triangle Inequality Theorem" ] } ## Verify the Triangle Inequality Theorem $$ \begin{aligned} &15 + 36 = 51 \ &51 > 41 \end{aligned} $$ ## Calculate the squares of the side lengths $$ \begin{aligned} &15^2 + 36^2 = 225 + 1296 = 1521 \ &41^2 = 1681 \end{aligned} $$ ## Apply the converse of the Pythagorean Theorem $$ \begin{aligned} &1521 eq 1681 \implies a^2 + b^2 eq c^2 \end{aligned} $$

(A) $15 + 36 > 41$, so the side lengths will form a triangle.

(B) $15 + 36 = 41$, so those lengths will not form a triangle.

(C) $15^2 + 36^2 = 1521$

(D) $41^2 = 1681$

(E) Since $a^2 + b^2 eq c^2$, it will not be a right triangle.

(F) $15^2 + 36^2 = 297$

(G) $41^2 = 82$

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

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QUESTION IMAGE

Question

Explanation:

Verify the Triangle Inequality Theorem

Calculate the squares of the side lengths

Apply the converse of the Pythagorean Theorem

Answer: