Question

1. find y.

triangle with points a, b, c, d. ac=27, ad=18, cb=24, db=y. cd is an angle bisector? multiple choice options: 14, 15, 16, 17

Explanation:

Step1: Apply the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if \(CD\) is the angle - bisector of \(\angle ACB\) in \(\triangle ABC\), then \(\frac{AC}{CB}=\frac{AD}{DB}\). Here, \(AC = 27\), \(CB=24\), \(AD = 18\), and \(DB=y\).
So, we have the proportion \(\frac{27}{24}=\frac{18}{y}\).

Step2: Cross - multiply to solve for \(y\)

Cross - multiplying gives \(27y=24\times18\).
First, calculate \(24\times18 = 432\). Then, \(y=\frac{432}{27}\).
Since \(432\div27 = 16\).

Answer:

16