Question

12
x
5
10
4\frac{1}{6}
9
6

Explanation:

Step1: Apply angle - bisector theorem

The angle - bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle. In the given triangle, if the angle is bisected, we have the proportion $\frac{12}{x}=\frac{10}{5}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{12}{x}=\frac{10}{5}$ gives us $10x = 12\times5$.

Step3: Solve for $x$

We have $10x=60$. Dividing both sides by 10, we get $x = 6$.

Answer:

6