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प्रश्न
∆ABC is such that AB = 3 cm, BC = 2 cm and CA = 2.5 cm. If ∆DEF ∼ ∆ABC and EF = 4 cm, then perimeter of ∆DEF is
विकल्प
7.5 cm
15 cm
22.5 cm
30 cm
उत्तर
Given: In ΔABC, AB = 3cm, BC = 2cm, CA = 2.5cm. `ΔDEF ∼ Δ ABC ` and EF = 4cm.
To find: Perimeter of ΔDEF.
We know that if two triangles are similar, then their sides are proportional
Since ΔABC and ΔDEF are similar,
`(AB)/(DE)=(BC)/(EF)=(CA)/(FD)`
`3/(DE)=2/4=2.5/(FD)`
`3/(DE)=2/4`...............(1)
`DE=6cm`
`2/4=2.5/(FD)`
`FD=5cm......................(2)
From (1) and (2), we get
Perimeter of ΔDEF = DE + EF + FD = 6 + 4 +5 = 15 cm
Hence the correct answer is `b`
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