Question

△def ~ △lmn
find ef.
108
140
135
169

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle DEF\sim\triangle LMN\), the ratios of their corresponding sides are equal. That is \(\frac{EF}{MN}=\frac{DE}{LM}\).

Step2: Substitute the known values

We know \(DE = 100\), \(LM=30\), and \(MN = 42\). Substituting into the proportion \(\frac{EF}{42}=\frac{100}{30}\).

Step3: Solve for \(EF\)

Cross - multiply: \(30\times EF=100\times42\). Then \(EF=\frac{100\times42}{30}\). Simplify \(\frac{100\times42}{30}=\frac{100\times14}{10}=140\).

Answer:

140