If two triangles are similar, their sides form a proportion.
[tex]\dfrac{3x+1}{12}=\dfrac{4x}{12+3}\\\\\dfrac{3x+1}{12}=\dfrac{4x}{15}\qquad|\text{cross\ multiply}\\\\15(3x+1)=12(4x)\qquad|\text{use distributive property}\\\\(15)(3x)+(15)(1)=48x\\\\45x+15=48x\qquad|\text{subtract 45x from both sides}\\\\15=3x\qquad|\text{divide both sides by 3}\\\\5=x\to x=5[/tex]
Answer: x = 5
