Question

given $\triangle abc \sim \triangle def$, $\overline{ab} = 5$, $\overline{df} = 6$, and $\overline{de} = 3$. what is the length of $\overline{ac}$?\
a 10\
c 8\
b $\frac{5}{2}$\
d 6

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{AC}{DF}\)

Step2: Substitute the given values

We know \(AB = 5\), \(DE=3\), and \(DF = 6\). Substituting into \(\frac{AB}{DE}=\frac{AC}{DF}\), we get \(\frac{5}{3}=\frac{AC}{6}\)

Step3: Solve for \(AC\)

Cross - multiply: \(3\times AC=5\times6\), so \(3AC = 30\). Then \(AC=\frac{30}{3}=10\)

Answer:

A. 10