The areas of two similar triangles are 16 cm^2 and 25 cm^2 respectively, then the ratio of their corresponding sides is ………
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
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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.
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