Question

determine whether the set of lengths forms a right, acute, or obtuse triangle. 13 cm., 12 cm., 5 cm.

Explanation:

Step1: Recall the Pythagorean theorem

For a triangle with side lengths \(a\), \(b\), \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}=c^{2}\), it is a right - triangle; if \(a^{2}+b^{2}>c^{2}\), it is an acute - triangle; if \(a^{2}+b^{2}

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

Calculate \(a^{2}+b^{2}\): \(5^{2}+12^{2}=25 + 144=169\). Calculate \(c^{2}\): \(13^{2}=169\).

Answer:

Since \(5^{2}+12^{2}=13^{2}\), the set of lengths \(13\mathrm{cm}\), \(12\mathrm{cm}\), \(5\mathrm{cm}\) forms a right - triangle.