Question

a triangle has sides with lengths of 42 kilometers, 56 kilometers, and 70 kilometers. 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 \(a = 42\), \(b = 56\), and \(c = 70\).

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

\(a^{2}=42^{2}=42\times42 = 1764\), \(b^{2}=56^{2}=56\times56 = 3136\). Then \(a^{2}+b^{2}=1764 + 3136=4900\).

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

\(c^{2}=70^{2}=70\times70 = 4900\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (as \(4900 = 4900\)), the triangle is a right - triangle.

Answer:

yes