Question

solve for a.
12
3
a
a = ?

Explanation:

Step1: Apply the geometric mean theorem (altitude-on-hypotenuse theorem)

The theorem states that in a right - triangle, the altitude \(a\) to the hypotenuse is the geometric mean of the segments of the hypotenuse. If the segments of the hypotenuse are \(x = 12\) and \(y=3\), then \(a=\sqrt{xy}\).

Step2: Substitute the values of \(x\) and \(y\)

Substitute \(x = 12\) and \(y = 3\) into the formula \(a=\sqrt{xy}\). So \(a=\sqrt{12\times3}\).

Step3: Simplify the expression

First, calculate \(12\times3=36\). Then \(\sqrt{36}=6\).

Answer:

\(6\)