Triangles ABC and CDE and similar with ABC being dilated larger. This means we can use ratios to help solve for x, and then solve fo AC.
[tex]\frac{84}{156-x} = \frac{7}{x}[/tex]
[tex]\frac{84x}{156-x} = 7[/tex]
[tex]84x = 7(156 - x)[/tex]
[tex]84x = 1092 - 7x[/tex]
[tex]91x = 1092[/tex]
[tex]x = 12[/tex]
So, from this problem we now know that x is equal to 12. We merely need to plug that into what is given for AC and solve for AC.
AC = 156 - 12
AC = 144
Therefore, A is equal to 144.
