Given:
The figure of a triangle.
To find:
The value of x.
Solution:
According to the triangle proportionality theorem, if a line segment divides the two sides of a triangle and parallel to the third side of the triangle, the it divides the two inclined sides proportionally.
Using triangle proportionality theorem, we get
![\dfrac{2x}{80}=\dfrac{27}{60}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B80%7D%3D%5Cdfrac%7B27%7D%7B60%7D)
![\dfrac{x}{40}=\dfrac{9}{20}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B40%7D%3D%5Cdfrac%7B9%7D%7B20%7D)
Multiply both sides by 40.
![x=\dfrac{9}{20}\times 40](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B9%7D%7B20%7D%5Ctimes%2040)
![x=9\times 2](https://tex.z-dn.net/?f=x%3D9%5Ctimes%202)
![x=18](https://tex.z-dn.net/?f=x%3D18)
Therefore, the value of x is 18.