Question

type the correct answer in the box. use numerals instead of words. find the missing side length, x. the value of the missing side length labeled as x is reset next

Explanation:

Step1: Apply the Angle - Bisector Theorem

The Angle - Bisector Theorem states that if \(AD\) is the angle bisector of \(\angle BAC\), then \(\frac{AB}{AC}=\frac{BD}{DC}\).
Given \(AB = 12\), \(AC = 20\), and \(DC=12\). Let \(BD=x\).
Substitute the values into the formula: \(\frac{12}{20}=\frac{x}{12}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(20x=12\times12\).
So, \(20x = 144\).
Then, \(x=\frac{144}{20}=7.2\).

Answer:

\(7.2\)