Question

do the segment lengths 15, 12, and 9 form a right triangle?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 9\), \(b = 12\), \(c = 15\).
Calculate \(a^{2}+b^{2}\): \(9^{2}+12^{2}=81 + 144=225\).
Calculate \(c^{2}\): \(15^{2}=225\).

Step2: Compare results

Since \(9^{2}+12^{2}=15^{2}\), the segments satisfy the Pythagorean theorem.

Answer:

Yes, the segment lengths 15, 12, and 9 form a right - triangle.