Question

a triangle has sides with lengths of 74 feet, 24 feet, and 70 feet. 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.

Step2: Identify the sides

Let \(a = 24\), \(b = 70\), and \(c = 74\).

Step3: Calculate \(a^{2}+b^{2}\)

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

Step4: Calculate \(c^{2}\)

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

Step5: Compare

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

Answer:

yes