Question

select the correct answer.
a triangular garden is to be split so that the angle at vertex b is bisected. this diagram was supplied by the landscape architect, but you do not have a way to measure the angles at b. you do have the given side lengths, so what is the length of side ad that will allow the angle at b to be bisected?
a. 4 m
b. 3 m
c. 5 m
d. 2 m

Explanation:

Step1: Apply Angle Bisector Theorem

The Angle Bisector Theorem states that $\frac{AD}{DC} = \frac{AB}{BC}$. Substitute the known values: $AD = x$, $DC = 4$, $AB = 6$, $BC = 8$.
$\frac{x}{4} = \frac{6}{8}$

Step2: Solve for $x$

Simplify the right-hand side and isolate $x$.
$x = \frac{6}{8} \times 4$
$x = 3$

Answer:

B. 3 m