ΔABC ~ ΔDEF and their areas are 16 cm2 and 81 cm2 respectively.If B

1.	ΔABC ~ ΔDEF and their areas are 16 cm2 and 81 cm2 respectively.If BC = 4 cm, then EF =(A) 5 cm (B) 4 cm (C) 11 cm (D) 9 cm
Answer» Correct option is (D) 9 cm \(\because\) \(\triangle ABC \sim \triangle DEF\) \(\therefore\) \(\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=(\frac{BC}{EF})^2\) \(\Rightarrow\)\((\frac{BC}{EF})^2=\frac{16}{81}\) (Given \(ar(\triangle ABC)=16\,cm^2\;\&\;ar(\triangle DEF)=81\,cm^2)\) \(\Rightarrow\) \(\frac{BC}{EF}=\sqrt{\frac{16}{81}}=\frac49\) \(\Rightarrow EF=\frac94BC\) \(=\frac94\times4=9\) \((\because BC=4\,cm)\) \(\therefore\) EF = 9 cm Correct option is: (D) 9 cm

ΔABC ~ ΔDEF and their areas are 16 cm2 and 81 cm2 respectively.If BC = 4 cm, then EF =(A) 5 cm (B) 4 cm (C) 11 cm (D) 9 cm

Answer»

Correct option is (D) 9 cm

\(\because\) \(\triangle ABC \sim \triangle DEF\)

\(\therefore\) \(\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=(\frac{BC}{EF})^2\)

\(\Rightarrow\)\((\frac{BC}{EF})^2=\frac{16}{81}\) (Given \(ar(\triangle ABC)=16\,cm^2\;\&\;ar(\triangle DEF)=81\,cm^2)\)

\(\Rightarrow\) \(\frac{BC}{EF}=\sqrt{\frac{16}{81}}=\frac49\)

\(\Rightarrow EF=\frac94BC\)

\(=\frac94\times4=9\) \((\because BC=4\,cm)\)

\(\therefore\) EF = 9 cm

Correct option is: (D) 9 cm