Question

tell whether a triangle with sides 18 cm, 24 cm, and 30 cm is acute, right or obtuse. right obtuse acute

Explanation:

Step1: Recall the Pythagorean theorem

Let \(a = 18\), \(b=24\), \(c = 30\) (where \(c\) is the longest side). The Pythagorean theorem states that 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 \(a^{2}+b^{2}\)

\(a^{2}=18^{2}=324\), \(b^{2}=24^{2}=576\), so \(a^{2}+b^{2}=324 + 576=900\).

Step3: Calculate \(c^{2}\)

\(c^{2}=30^{2}=900\).

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

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(900 = 900\)), the triangle is a right - triangle.

Answer:

A. right