Question

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 1

AC = 25 units

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.

`\frac{\text{Hypotenuse}}{\text{leg}}=\frac{\text{leg}}{\text{Projection}}`

`(AC)/(BC)=(BC)/(DC)`

`(x)/(10)=(10)/(4)`

x =
`(10* 10)/(4)`

x = 25 units