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Question
If it is given that ΔАBС ~ ΔEDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = ______ and EF = ______.
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Solution
If it is given that ΔАBС ~ ΔEDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = 6.25 cm and EF = 16.8 cm.
Explanation:
Since ΔABC ~ ΔEDF, corresponding sides are proportional:
`(AB)/(DE) = (BC)/(DF) = (AC)/(EF)`
Let the common ratio = `(AB)/(DE) = 5/12`.
`BC = DF xx (AB)/(DE)`
= `15 × 5/12`
= `75/12`
= 6.25 cm
`EF = AC xx (DE)/(AB)`
= `7 xx 12/5`
= `84/5`
= 16.8 cm
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