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).

Step2: Identify sides

Let \(a = 5\), \(b = 6\), \(c = 10\).

Step3: Calculate \(a^2 + b^2\)

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

Step4: Calculate \(c^2\)

\(10^2 = 100\).

Step5: Compare results

Since \(61
eq 100\), the sides do not satisfy the Pythagorean theorem.

Answer:

No, the side lengths 5, 6, 10 do not form a right triangle.