Question

tell whether a triangle with sides 6 cm, 12 cm, and 17 cm is acute, right or obtuse. acute right obtuse

Explanation:

Step1: Recall the Pythagorean - related rule

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

Step2: Identify \(a\), \(b\), and \(c\)

Let \(a = 6\), \(b = 12\), and \(c = 17\).

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

\(a^{2}=6^{2}=36\), \(b^{2}=12^{2}=144\), so \(a^{2}+b^{2}=36 + 144=180\). And \(c^{2}=17^{2}=289\).

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(180<289\) (i.e., \(a^{2}+b^{2}

Answer:

obtuse