Question

Find the value of x using the Triangle Angle Bisector Theorem. Show all Work

Answer 1

The Angle Bisector Theorem states that:

`(|AB|)/(|AC|)=(|BD|)/(|CD|)\text{.}`

From the diagram, we see that:

• |AB| = 11,

,

• |AC| = 9,

,

• |BD| = x,

,

• |CD| = 7.

Replacing these data in the equation above, we have:

`(11)/(9)=(x)/(7)\text{.}`

Solving for x, we get:

`x=7\cdot(11)/(9)=(77)/(9).`

Answer

`x=(77)/(9)`