Question

a triangle has sides with lengths of 16 inches, 18 inches, and 25 inches. is it a right triangle?

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 16\), \(b = 18\), \(c = 25\).

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

• Calculate \(a^{2}+b^{2}\):

\(a^{2}+b^{2}=16^{2}+18^{2}=256 + 324=580\)

• Calculate \(c^{2}\):

\(c^{2}=25^{2}=625\)

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

Since \(580
eq625\) (i.e., \(a^{2}+b^{2}
eq c^{2}\)), the triangle is not a right - triangle.

Answer:

no