Question

12 find the value of x. 10 16 14 9

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. So, we have $\frac{8}{6}=\frac{12}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{8}{6}=\frac{12}{x}$ gives us $8x = 12\times6$.

Step3: Simplify the right - hand side

$12\times6=72$, so the equation becomes $8x = 72$.

Step4: Solve for x

Dividing both sides of the equation $8x = 72$ by 8, we get $x=\frac{72}{8}=9$.

Answer:

9