Question

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1. determine if the following side lengths form a right triangle: 8, 6, 10. explain your work

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the longest side. Here, \(c = 10\), \(a = 6\), \(b = 8\).

Step2: Calculate \(a^2 + b^2\)

\(6^2 + 8^2 = 36 + 64 = 100\)

Step3: Calculate \(c^2\)

\(10^2 = 100\)

Step4: Compare results

Since \(6^2 + 8^2 = 10^2\), the sides satisfy the Pythagorean theorem.

Answer:

Yes, the side lengths 8, 6, 10 form a right triangle because \(6^2 + 8^2 = 10^2\) (by the Pythagorean theorem).