Question

a triangle has sides with lengths of 36 kilometers, 47 kilometers, and 57 kilometers. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\).
Let \(a = 36\), \(b = 47\), and \(c = 57\). Calculate \(a^{2}+b^{2}\) and \(c^{2}\).
\[a^{2}=36^{2}=1296\]
\[b^{2}=47^{2}=2209\]
\[a^{2}+b^{2}=1296 + 2209=3505\]
\[c^{2}=57^{2}=3249\]

Step2: Compare results

Since \(a^{2}+b^{2}=3505
eq3249 = c^{2}\), the triangle is not a right - triangle.

Answer:

no