Question

What is the length of AC ?

Answer 1

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.

$\frac{84}{156-x} = \frac{7}{x}$
$\frac{84x}{156-x} = 7$
$84x = 7(156 - x)$
$84x = 1092 - 7x$
$91x = 1092$
$x = 12$
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.