Answer:
The correct option is 3.
Step-by-step explanation:
The corresponding sides of similar triangles are similar.
It is given that two triangles are similar. One triangle are lengths 2, 4 and 6 and another triangle has sides of lengths 3, 6 and x.
Since the corresponding sides of similar triangles are proportional, therefore
[tex]\frac{2}{3}=\frac{4}{6}=\frac{6}{x}[/tex]
[tex]\frac{2}{3}=\frac{2}{3}=\frac{6}{x}[/tex]
[tex]\frac{2}{3}=\frac{6}{x}[/tex]
Use cross multiplication.
[tex]2\times x=6\times 3[/tex]
[tex]2x=18[/tex]
Divide both sides by 2.
[tex]x=\frac{18}{2}[/tex]
[tex]x=9[/tex]
Therefore the correct option is 3.
