Question

practice
①

Explanation:

Step1: Use geometric - mean theorem

In a right - triangle, if the altitude \(x\) is drawn to the hypotenuse, then \(x^{2}=9\times4\).

Step2: Solve for \(x\)

\[x = \sqrt{9\times4}=\sqrt{36}=6\]

Step3: Use Pythagorean theorem for finding \(y\)

\[y=\sqrt{9^{2}+6^{2}}=\sqrt{81 + 36}=\sqrt{117}=3\sqrt{13}\]

Step4: Use Pythagorean theorem for finding \(z\)

\[z=\sqrt{6^{2}+4^{2}}=\sqrt{36+16}=\sqrt{52}=2\sqrt{13}\]

Answer:

\(x = 6\), \(y = 3\sqrt{13}\), \(z = 2\sqrt{13}\)