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

Explanation:

Step1: Set up 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 $\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}$. Using $\frac{BC}{EF}=\frac{AB}{DE}$, we get $\frac{6}{42}=\frac{2}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{6}{42}=\frac{2}{x}$ gives us $6x = 2\times42$.

Step3: Solve for $x$

First, calculate $2\times42 = 84$. Then, we have the equation $6x=84$. Divide both sides by 6: $x=\frac{84}{6}=14$.

Answer:

14