If $\vartriangle ABC\sim\vartriangle RPQ,\ AB=3\ cm,\ BC=5\ cm,\ AC=6\ cm,\  RP=6\ cm\ and\ PQ=10\ cm$, then find $QR$.

Given: $\vartriangle ABC\sim\vartriangle RPQ,\ AB=3\ cm,\ BC=5\ cm,\ AC=6\ cm,\ RP=6\ cm\ and\ PQ=10\ cm$ .

To do: To find $QR$.

Solution:  

$\because\ \vartriangle ABC\sim\vartriangle PQR$

If two triangles are similar, then its corresponding sides are proportional.

$\frac{RP}{AB}=\frac{PQ}{BC}=\frac{QR}{AC}$

$\Rightarrow \frac{6}{3}=\frac{10}{5}=\frac{QR}{6}$

$\Rightarrow \frac{QR}{6}=\frac{6}{3}$

$\Rightarrow QR=\frac{6\times6}{3}$

$\Rightarrow QR=12$

Thus $QR=12\ cm$.