Question

△abc and △def are similar. find the missing side length. (the triangles are not drawn to scale.)

Explanation:

Step1: Set up the proportion

Since $\triangle ABC$ and $\triangle DEF$ are similar, the ratios of corresponding sides are equal. Let the missing side length be $x$. We have the proportion $\frac{AB}{DE}=\frac{AC}{DF}$. Substituting the given values, $\frac{2}{18}=\frac{4}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{2}{18}=\frac{4}{x}$ gives us $2x = 18\times4$.

Step3: Solve for $x$

First, calculate $18\times4 = 72$. Then, for the equation $2x=72$, divide both sides by 2. So $x=\frac{72}{2}=36$.

Answer:

36