Answer:
[tex]x=2[/tex]
Step-by-step explanation:
The two triangles are similar. So that means it's corresponding sides are proportional.
So this means we can find x using the equation:
[tex]\frac{4x+2}{2x+16}=\frac{18}{36}[/tex]
Simplify:
[tex]\frac{4x+2}{2x+16}=\frac{1}{2}[/tex]
Cross multiply:
[tex]2(4x+2)=1(2x+16)[/tex]
Distribute/multiply:
[tex]8x+4=2x+16[/tex]
Subtract [tex]2x[/tex] on both sides:
[tex]6x+4=16[/tex]
Subtract [tex]4[/tex] on both sides:
[tex]6x=12[/tex]
Divide both sides by 6:
[tex]x=\frac{12}{6}[/tex]
Simplify:
[tex]x=2[/tex]
