Question

1. in the figure, bd = 12 and ad = 16. what is the length of \overline{dc}?

note: figure not drawn to scale.
\overline{dc} =

Explanation:

Step1: Use the geometric mean theorem

In a right - triangle \(ABC\) with right - angle at \(B\) and altitude \(BD\) to the hypotenuse \(AC\), the theorem states that \(BD^{2}=AD\times DC\).

Step2: Substitute the given values

We know that \(BD = 12\) and \(AD=16\). Plugging these into the formula \(BD^{2}=AD\times DC\), we get \(12^{2}=16\times DC\).

Step3: Solve for \(DC\)

First, calculate \(12^{2}=144\). Then the equation becomes \(144 = 16\times DC\). Divide both sides by 16: \(DC=\frac{144}{16}\).

Answer:

\(9\)