Given:
The given figure of a triangle.
To find:
The value of x.
Solution:
According to the angle bisector theorem, the angle bisector of a triangle divides the opposite side in two parts that are proportional to other two sides of the triangle.
Using angle bisector theorem, we get
[tex]\dfrac{2x-5}{21}=\dfrac{10}{24-10}[/tex]
[tex]\dfrac{2x-5}{21}=\dfrac{10}{14}[/tex]
[tex]\dfrac{2x-5}{21}=\dfrac{5}{7}[/tex]
Multiply both sides by 21.
[tex]\dfrac{2x-5}{21}\times 21=\dfrac{5}{7}\times 21[/tex]
[tex]2x-5=15[/tex]
[tex]2x=15+5[/tex]
[tex]2x=20[/tex]
Divide both sides by 2.
[tex]x=\dfrac{20}{2}[/tex]
[tex]x=10[/tex]
Therefore, the value of x is 10.
