$$\scriptsize \text{Note: Figure not drawn to scale.}$$

On $\overline{AD}$ above, $AB=CD$. What is the length of $\overline{AC}$ ?

Summary Submit

Since $AB=CD$,

$$x-2=3x-12$$ $$10=2x$$ $$x=5$$

Substituting this into our expressions in the figure,

$$AB=3, BC=5, CD=3$$ $$AC=AB+BC$$ $$AC=3+5$$ $$AC=\boxed{8}$$