Question

mrs. ibarra wants to create a right triangle for a geometry test. she plans to use 15, 36, and 41 as side lengths. choose four correct answers regarding the side lengths mrs. ibarra chose. 15² + 36² = 1521 15² + 36² = 297 15 + 36 = 41, so those lengths will not form a triangle. 41² = 82 41² = 1681 15 + 36 > 41, so the side lengths will form a triangle. since a² + b² ≠ c², it will not be a right triangle.

Explanation:

Step1: Calculate \(15^{2}+36^{2}\)

$$
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$$

Step2: Calculate \(41^{2}\)

$$ 41^{2}=1681 $$

Step3: Check triangle - inequality

For three side - lengths \(a = 15\), \(b = 36\), \(c = 41\), we check \(a + b>c\), \(a + c>b\), \(b + c>a\).
Since \(15+36 = 51>41\), \(15 + 41=56>36\), \(36+41 = 77>15\), the side - lengths will form a triangle.

Step4: Check Pythagorean theorem

We check if \(a^{2}+b^{2}=c^{2}\). Here \(a = 15\), \(b = 36\), \(c = 41\)
\(a^{2}+b^{2}=15^{2}+36^{2}=1521\) and \(c^{2}=41^{2}=1681\)
Since \(15^{2}+36^{2}
eq41^{2}\), it is not a right - triangle.

Answer:

\(15^{2}+36^{2}=1521\), \(41^{2}=1681\), \(15 + 36>41\) so the side lengths will form a triangle, Since \(a^{2}+b^{2}
eq c^{2}\), it will not be a right triangle.