Question

△abc y △pqr son semejantes. hallar la longitud lateral desconocida. (los triángulos no están dibujados a escala.)

Explanation:

Step1: Find the scale - factor

Since the two triangles $\triangle ABC$ and $\triangle PQR$ are similar, the ratios of their corresponding sides are equal. We can find the scale - factor by comparing the known corresponding sides. Let's compare side $AB = 2$ and side $PQ=16$. The scale - factor $k=\frac{PQ}{AB}=\frac{16}{2} = 8$.

Step2: Calculate the unknown side

We want to find the side corresponding to $BC = 4$. Let the unknown side be $x$. Using the scale - factor, we know that $\frac{x}{BC}=k$. Substituting $BC = 4$ and $k = 8$, we get $x=k\times BC$. So $x=8\times4=32$.

Answer:

32