Question

If ∆ABC and ∆DEF are similar triangles such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm, write the perimeter of ∆DEF.

Answer 1

GIVEN: ΔABC and ΔDEF are similar triangles such that AB = 3 cm, BC = 2 cm, CA = 2.5 cm and EF = 4 cm.

TO FIND: Perimeter of ΔDEF.

We know that if two triangles are similar then their corresponding sides are proportional.

Hence, `(AB)/(DE)=(BC)/(EF)=(CA)/(FD)`

Substituting the values, we get

`(AB)/(BC)=(DE)/(EF)`

`3/2=(DE)/4`

`DE=6  cm`........(1)

Similarly,

`(CA)/(BC)=(DF)/(EF)`

`2.5/2=(DF)/(4)`

`DF= 5  cm`...........(2)

Perimeter of `ΔDEF = DE +EF+DF`

`=6+4+5`

`= 15  cm`