Question

using the provided diagram, which of the following is a correct way to substitute the side lengths into the pythagorean theorem? m² + g² = s²; s² + g² = m²; g² + s² = m²; two of these are correct.

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), the Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\). In the given right - triangle, the legs have lengths \(s\) and \(y\), and the hypotenuse has length \(m\).

Step2: Apply the theorem

Substituting the side lengths into the Pythagorean Theorem, we get \(s^{2}+y^{2}=m^{2}\).

Answer:

\(s^{2}+y^{2}=m^{2}\)