Question

a triangle has sides with lengths of 54 miles, 73 miles, and 43 miles. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). The hypotenuse is the longest side. Here \(c = 73\), \(a = 54\), \(b = 43\).

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

\(a^{2}+b^{2}=54^{2}+43^{2}=2916 + 1849=4765\).

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

\(c^{2}=73^{2}=5329\).

Step4: Compare

Since \(a^{2}+b^{2}=4765
eq5329 = c^{2}\), it is not a right - triangle.

Answer:

no