Answer:
The correct option is 3. The length of XC is 30.
Step-by-step explanation:
It is given that triangle ABC and triangle XYC are similar.
According to the properties of similar triangles, then corresponding sides of similar triangles are congruent.
In triangle ABC and triangle XYC,
[tex]\frac{AB}{XY}=\frac{BC}{YC}=\frac{AC}{XC}[/tex]
Let the length of XC be x.
From the below figure it is notices that
[tex]AC=AX+XC=18+x[/tex]
[tex]BC=BY+YC=6+10=16[/tex]
[tex]\frac{16}{10}=\frac{18+x}{x}[/tex]
[tex]16x=180+10x[/tex]
[tex]6x=180[/tex]
[tex]x=30[/tex]
Therefore correct option is 3. The length of XC is 30.
