Question

In the diagram, \overline {BC} BC is an altitude of \DeltaΔABD. To the nearest whole unit, what is the length of \overline {CD} CD ?

Answer 1

To answer this question we will use the right triangle altitude theorem.

Using the right triangle altitude theorem we get that:

$BC=\sqrt{DC\times CA}.$

Substituting BC=16 and CA=23 in the above result we get:

$16=\sqrt{DC\times23}.$

Therefore:

$256=23DC.$

Dividing the above result by 23 we get:

$\begin{gathered} \frac{256}{23}=\frac{23DC}{23}, \\ DC=\frac{256}{23}\approx11. \end{gathered}$

Answer: Option D.