Q. 163.8( 19 Votes )

Prove that the ra

Answer :

Let ∆ ABC and ∆ DEF be two similar triangles, i.e., ∆ ABC ∆ DEF.

Ratio of all the corresponding sides of ∆ ABC and ∆ DEF are equal.



Let these ratios be equal to some number α.



AB = α DE, BC = α EF, AC = α DF ……….(i)


Now, perimeter of ∆ ABC = AB + BC + AC


= α DE + α EF + α DF [ From (i)]


= α (DE + EF + DF)


= α (perimeter of ∆ DEF)




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