Answer:
x = 7
Step-by-step explanation:
The parameters of the triangle having bisected angle are;
The length of the opposite and adjacent side of one of the halves of the bisected angle = 6 and 14 respectively
The length of the opposite and adjacent side of the other half of the bisected angle = (3·x - 12) and 21 respectively
By the angle bisector theorem, we have;
[tex]\dfrac{14}{6} = \dfrac{21}{3\cdot x - 12}[/tex]
Simplifying, we get;
[tex]\dfrac{14}{6} = \dfrac{2 \times 7}{2 \times 3} = \dfrac{7}{3}[/tex]
[tex]\dfrac{21}{3\cdot x - 12} = \dfrac{3 \times 7}{3 \times (x - 4)} = \dfrac{7}{x - 4}[/tex]
[tex]\dfrac{7}{3} = \dfrac{7}{ x - 4}[/tex]
7 × (x - 4) = 3 × 7
∴ x - 4 = 3
x = 3 + 4 = 7
x = 7.
