Question

the sides of a triangle have lengths 2, 3, and 4. what kind of triangle is it? acute right obtuse

Explanation:

Step1: Recall the Pythagorean - related rules

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}Here \(a = 2\), \(b = 3\), \(c = 4\).

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

Calculate \(a^{2}+b^{2}\): \(a^{2}=2^{2}=4\), \(b^{2}=3^{2}=9\), so \(a^{2}+b^{2}=4 + 9=13\).
Calculate \(c^{2}\): \(c^{2}=4^{2}=16\).

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

Since \(a^{2}+b^{2}=13\) and \(c^{2}=16\), and \(13<16\) (i.e., \(a^{2}+b^{2}

Answer:

obtuse