The areas of two similar triangles are 16 cm2 and 25 cm2 respective

1.	The areas of two similar triangles are 16 cm2 and 25 cm2 respectively, then the ratio of their corresponding sides is ………(A) 5 : 4 (B) 4 : 5 (C) 16 : 25 (D) 25 : 16
Answer» Correct option is (B) 4 : 5 Let similar triangles are \(\triangle ABC\;\&\;\triangle DEF\) Also let \(ar(\triangle ABC)=16\,cm^2\;\&\) \(ar(\triangle DEF)=25\,cm^2\) \(\because\) \(\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=(\frac{AB}{DE})^2\) \(\therefore\) \((\frac{AB}{DE})^2=\frac{16}{25}\) \(\Rightarrow\) \(\frac{AB}{DE}=\sqrt{\frac{16}{25}}=\frac45\) \(\therefore AB:DE=4:5\) Hence, the ratio of corresponding sides of given triangle is 4:5. Correct option is: (B) 4 : 5

The areas of two similar triangles are 16 cm2 and 25 cm2 respectively, then the ratio of their corresponding sides is ………(A) 5 : 4 (B) 4 : 5 (C) 16 : 25 (D) 25 : 16

Answer»

Correct option is (B) 4 : 5

Let similar triangles are \(\triangle ABC\;\&\;\triangle DEF\)

Also let \(ar(\triangle ABC)=16\,cm^2\;\&\)

\(ar(\triangle DEF)=25\,cm^2\)

\(\because\) \(\frac{ar(\triangle ABC)}{ar(\triangle DEF)}=(\frac{AB}{DE})^2\)

\(\therefore\) \((\frac{AB}{DE})^2=\frac{16}{25}\)

\(\Rightarrow\) \(\frac{AB}{DE}=\sqrt{\frac{16}{25}}=\frac45\)

\(\therefore AB:DE=4:5\)

Hence, the ratio of corresponding sides of given triangle is 4:5.

Correct option is: (B) 4 : 5