Question

if $\triangle abc \sim \triangle amn$ and $am = 6$, $mb = 4$, $an = 8$, then what is the value of $ac$?
options: 11, 13.3, 15.3, 15

Explanation:

Step1: Find AB length

AB = AM + MB = 6 + 4 = 10.

Step2: Set up proportion (similar triangles)

For similar triangles \( \triangle ABC \sim \triangle AMN \), the ratios of corresponding sides are equal: \( \frac{AM}{AB} = \frac{AN}{AC} \).
Substitute values: \( \frac{6}{10} = \frac{8}{AC} \).

Step3: Solve for AC

Cross - multiply: \( 6 \times AC = 10 \times 8 \).
\( 6AC = 80 \).
\( AC=\frac{80}{6}\approx13.3 \).

Answer:

13.3