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Question
If ∆ABC ∼ ∆DEF such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm, BC = 4 cm, then perimeter of ∆ABC is
Options
18 cm
20 cm
12 cm
15 cm
Solution
Given: ΔABC and ΔDEF are similar triangles such that DE = 3cm, EF = 2cm, DF = 2.5cm and BC = 4cm.
To find: Perimeter of ΔABC.
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)`
`(AB)/4=3/2`
`AB=6cm`..................(1)
Similarly,
`(CA)/(BE)=(DF)/(EF)`
`(CA)/4=2.5/2`
`CA=5cm`
Perimeter of Δ ABC = AB+BC+CA
= 6+4+5
= 15 cm
Hence the correct option is `d`
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