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=√(DC* CA).`

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

`16=√(DC*23).`

Therefore:

`256=23DC.`

Dividing the above result by 23 we get:

`\begin{gathered} (256)/(23)=(23DC)/(23), \\ DC=(256)/(23)\approx11. \end{gathered}`

Answer: Option D.