Question

△def ~ △lmn

Explanation:

Step1: Set up the proportion

Since \(\triangle DEF\sim\triangle LMN\), the ratios of corresponding sides are equal. Let the unknown side \(LM = x\). The proportion is \(\frac{DF}{LN}=\frac{DE}{LM}\).

Step2: Substitute the values

We know \(DF = 204\), \(LN=60\), and \(DE = 289\). Substituting into the proportion gives \(\frac{204}{60}=\frac{289}{x}\).

Step3: Cross - multiply

Cross - multiplying gives \(204x=60\times289\).

Step4: Solve for \(x\)

First, calculate \(60\times289 = 17340\). Then \(x=\frac{17340}{204}\).

Step5: Simplify the fraction

\(\frac{17340\div12}{204\div12}=\frac{1445}{17}=85\).

Answer:

\(85\)