what is the length of $overline{ac}$?\n3 ft\n4 ft\n18 ft\n12 ft

Answer:

D. 12 ft

Explanation:

Step1: Identify similar triangles

$\triangle BMN$ and $\triangle BAC$ are similar.

Step2: Set up proportion

Since $\frac{BM}{BA}=\frac{BN}{BC}=\frac{MN}{AC}$, and $\frac{BM}{BA}=\frac{4}{4 + 4}=\frac{1}{2}$, $\frac{BN}{BC}=\frac{3}{3+3}=\frac{1}{2}$. Also, $\frac{MN}{AC}=\frac{1}{2}$, given $MN = 6$ ft.

Step3: Solve for $AC$

Let $AC=x$. Then $\frac{6}{x}=\frac{1}{2}$, cross - multiplying gives $x = 12$ ft.