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Question
If ∆ABC ∼ ∆DEF such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of ∆DEF is 25 cm, then the perimeter of ∆ABC is
Options
36 cm
30 cm
34 cm
35 cm
Solution
Given: ΔABC is similar to ΔDEF such that AB= 9.1cm, DE = 6.5cm. Perimeter of ΔDEF is 25cm.
To find: Perimeter of ΔABC.
We know that the ratio of corresponding sides of similar triangles is equal to the ratio of their perimeters.
Hence,
`(AB)/(DE)=(BC)/(EF)=(AC)/(DE)=(P1)/(P2)`
`(AB)/(DE)=(P(Δ ABC))/(P(Δ DEF))`
`9.1/6.5=(P(Δ ABC))/25`
`P(Δ ABC)=(9.1xx25)/6.5`
`P(Δ ABC)=35cm`
Hence the correct answer is `d`
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