Question

a triangle has sides with lengths of 18 inches, 84 inches, and 85 inches. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 18\), \(b = 84\), and \(c = 85\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=18^{2}=324\), \(b^{2}=84^{2}=7056\).
\(a^{2}+b^{2}=324 + 7056=7380\).
Calculate \(c^{2}\):
\(c^{2}=85^{2}=7225\).

Step2: Compare results

Since \(a^{2}+b^{2}=7380
eq7225 = c^{2}\), the triangle is not a right - triangle.

Answer:

no