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 $QR=12\ cm$.
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