Question

a triangle has sides with lengths of 70 feet, 74 feet, and 24 feet. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 24\), \(b = 70\) and \(c = 74\).

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

\(a^{2}+b^{2}=24^{2}+70^{2}=576 + 4900=5476\).

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

\(c^{2}=74^{2}=5476\).

Step4: Compare

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

Answer:

yes