Question

use geometric mean to solve for p, q & h in the problems below.

1. p = 12 q = 3 h =?
2. p = 5 q =? h = 100

Explanation:

Step1: Recall the geometric mean formula for right - angled triangles

In a right - angled triangle, the altitude \(h\) to the hypotenuse is the geometric mean of the segments \(p\) and \(q\) of the hypotenuse. The formula is \(h=\sqrt{pq}\).

Step2: Substitute the values of \(p = 12\) and \(q = 3\) into the formula

For problem 11, we have \(h=\sqrt{12\times3}\).
First, calculate \(12\times3 = 36\). Then, \(\sqrt{36}=6\).

For problem 12, using the same formula \(h=\sqrt{pq}\), we can rewrite it as \(h^{2}=pq\). Given \(p = 5\) and \(h = 100\), we substitute these values into the equation \(100^{2}=5q\).
First, calculate \(100^{2}=10000\). Then, solve for \(q\): \(q=\frac{10000}{5}=2000\).

Answer:

1. \(h = 6\)
2. \(q = 2000\)