Question

1. determine if the following side lengths form a right triangle: 5, 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, \(a = 5\), \(b = 6\), \(c = 10\).

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

\(5^2 + 6^2 = 25 + 36 = 61\)

Step3: Calculate \(c^2\)

\(10^2 = 100\)

Step4: Compare results

Since \(61
eq 100\), \(a^2 + b^2
eq c^2\).

Answer:

The side lengths 5, 6, 10 do not form a right triangle because \(5^2 + 6^2
eq 10^2\) (25 + 36 = 61 ≠ 100), so the Pythagorean theorem is not satisfied.