Question

11 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 3m

Explanation:

Step1: Apply angle - bisector theorem

The angle - bisector theorem states that if \(BD\) is the angle - bisector of \(\angle ABC\) in \(\triangle ABC\), then \(\frac{AB}{BC}=\frac{AD}{DC}\).

Step2: Substitute given values

We know that \(AB = 6\) m, \(BC = 8\) m, and \(DC=4\) m. Substituting into \(\frac{AB}{BC}=\frac{AD}{DC}\), we get \(\frac{6}{8}=\frac{x}{4}\).

Step3: Solve for \(x\)

Cross - multiply: \(8x=6\times4\), so \(8x = 24\). Then \(x=\frac{24}{8}=3\) m.

Answer:

3 m