Question

the sides of a triangle have lengths 4, 9, and 12. what kind of triangle is it? acute right obtuse

Explanation:

Step1: Recall the Pythagorean - related rules

Let \(a = 4\), \(b = 9\), and \(c = 12\) (where \(c\) is the longest side). For a right - triangle, \(a^{2}+b^{2}=c^{2}\), for an acute - triangle \(a^{2}+b^{2}>c^{2}\), and for an obtuse - triangle \(a^{2}+b^{2}

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

\(a^{2}=4^{2}=16\), \(b^{2}=9^{2}=81\), so \(a^{2}+b^{2}=16 + 81=97\). And \(c^{2}=12^{2}=144\).

Step3: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(97<144\), i.e., \(a^{2}+b^{2}

Answer:

obtuse