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.
