Answer:
[tex]x=18{\frac{2}{3}}[/tex]
Step-by-step explanation:
It is given that the segment is parallel to one side of the triangle, therefore using the proportionality theorem, we get
[tex]\frac{x}{x+x+7}=\frac{16}{16+22}[/tex]
⇒[tex]\frac{x}{2x+7}=\frac{16}{38}[/tex]
⇒[tex]\frac{x}{2x+7}=\frac{8}{19}[/tex]
Upon cross multiplying, we have
⇒[tex]19x=16x+56[/tex]
⇒[tex]3x=56[/tex]
⇒[tex]x=18{\frac{2}{3}}[/tex]
Thus, the value of x is [tex]18{\frac{2}{3}}[/tex].
Hence, option B is correct.
