Question

using the provided diagram, which of the following is a correct way to substitute the side lengths into the pythagorean theorem? n² + m² = p², two of these are correct., m² + n² = p², p² + m² = n²

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(m\), \(n\) (legs) and \(p\) (hypotenuse), the Pythagorean theorem states that the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Step2: Identify hypotenuse and legs

In the given right - triangle, \(m\) and \(n\) are the legs and \(p\) is the hypotenuse.

Step3: Write the Pythagorean equation

The correct equation is \(m^{2}+n^{2}=p^{2}\).

Answer:

\(m^{2}+n^{2}=p^{2}\)