Question

use geometric mean to solve for p, q & h in the problems below. 11. p = 12 q = 3 h =? 12. p = 5 q =? h = 100 13. x = 14. x = y =

Explanation:

Problem 11

Step1: Recall the geometric mean formula for the altitude

The formula for the altitude \(h\) in a right - triangle (formed by the segments \(p\) and \(q\) of the hypotenuse) is \(h=\sqrt{pq}\).
Given \(p = 12\) and \(q=3\).

Step2: Substitute the values into the formula

\(h=\sqrt{12\times3}=\sqrt{36}\)

Step1: Recall the geometric mean formula for the altitude

The formula \(h=\sqrt{pq}\), we can re - arrange it to solve for \(q\). Squaring both sides gives \(h^{2}=pq\), so \(q=\frac{h^{2}}{p}\)
Given \(p = 5\) and \(h = 100\)

Step2: Substitute the values into the formula

\(q=\frac{100^{2}}{5}=\frac{10000}{5}\)

Step1: Recall the geometric mean formula for the altitude

The formula for the altitude \(x\) in a right - triangle (formed by the segments \(9\) and \(3\) of the hypotenuse) is \(x=\sqrt{9\times3}\)

Answer:

\(h = 6\)

Problem 12