Question

m, p, and z represent the lengths of the three sides of this right - triangle. select all the equations that represent the relationship between m, p, and z.

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Here, assuming \(m\) is the hypotenuse (the longest side opposite the right - angle) and \(p\) and \(z\) are the legs. The Pythagorean theorem is \(p^{2}+z^{2}=m^{2}\), which can also be written as \(z^{2}+p^{2}=m^{2}\), \(m^{2}=p^{2}+z^{2}\), \(m^{2}=z^{2}+p^{2}\).

Answer:

B. \(m^{2}=p^{2}+z^{2}\), C. \(m^{2}=z^{2}+p^{2}\), E. \(z^{2}+p^{2}=m^{2}\), F. \(p^{2}+z^{2}=m^{2}\)