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प्रश्न
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.
उत्तर
GIVEN: ΔABC and ΔDEF are similar triangles such that AB = 3cm, BC = 2cm, CA = 2.5cm and EF = 4cm.
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= 5cm`...........(2)
P[erimeter of `Δ DEF = DE +EF+DF`
`=6+4+5`
`= 15 cm`
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