Question

solve for the variable.
10.

Explanation:

Step1: Apply Angle Bisector Theorem

The Angle Bisector Theorem states that if a bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides. So, $\frac{18}{24}=\frac{x}{9}$.

Step2: Cross - Multiply to Solve for \(x\)

Cross - multiplying gives us \(24x = 18\times9\). First, calculate \(18\times9 = 162\). Then, we have the equation \(24x=162\).

Step3: Solve for \(x\)

Divide both sides of the equation by 24: \(x=\frac{162}{24}\). Simplify the fraction by dividing both the numerator and the denominator by 6, we get \(x = \frac{27}{4}=6.75\).

Answer:

\(x = \frac{27}{4}\) (or \(x = 6.75\))