Question

a triangle has sides with lengths of 56 yards, 70 yards, and 42 yards. 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 \(c = 70\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=42^{2}=42\times42 = 1764\)
\(b^{2}=56^{2}=56\times56=3136\)
\(a^{2}+b^{2}=1764 + 3136=4900\)
Calculate \(c^{2}\):
\(c^{2}=70^{2}=70\times70 = 4900\)
Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(4900=4900\)).

Answer:

yes