Question

1. determine if the following side lengths form a right triangle: 5, 12, 13. 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, \(a = 5\), \(b = 12\), \(c = 13\).

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

\(5^2 + 12^2 = 25 + 144 = 169\)

Step3: Calculate \(c^2\)

\(13^2 = 169\)

Step4: Compare results

Since \(5^2 + 12^2 = 13^2\), the sides satisfy the Pythagorean theorem.

Answer:

The side lengths 5, 12, 13 form a right triangle because \(5^2 + 12^2 = 13^2\) (25 + 144 = 169), satisfying the Pythagorean theorem.