Given right triangle ABC with altitude BD drawn to hypotenuse AC. If BC= 10 and DC = 4, what is the length of AC? (Note: the figure is not drawn to scale.)

Answer:
AC = 25 units
Step-by-step explanation:
Length of BC = 10 units
Length of DC = 4 units
We will use geometric mean theorem in the given right triangle to get the length of side AC.
[tex]\frac{\text{Hypotenuse}}{\text{leg}}=\frac{\text{leg}}{\text{Projection}}[/tex]
[tex]\frac{AC}{BC}=\frac{BC}{DC}[/tex]
[tex]\frac{x}{10}=\frac{10}{4}[/tex]
x = [tex]\frac{10\times 10}{4}[/tex]
x = 25 units