question_answer

Given \[\Delta \,ABC\sim \Delta \,PQR\], if \[\frac{AB}{PQ}=\frac{1}{3}\], then find \[\frac{ar\,\,\Delta \,ABC}{ar\,\,\Delta \,\,PQR}\].        

Answer:

Given, \[\Delta \text{ }ABC\tilde{\ }\Delta \text{ }PQR\]

And                  \[\frac{AB}{PQ}=\frac{1}{3}\]

Now         \[\frac{ar(\Delta \,ABC)}{ar(\Delta \,PQR)}=\frac{A{{B}^{2}}}{P{{Q}^{2}}}\]

\[={{\left( \frac{1}{3} \right)}^{2}}=\frac{1}{9}\]