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प्रश्न
D and E are the points on the sides AB and AC respectively of a ΔABC such that: AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.
उत्तर
We have,
`"AD"/"DB"=8/12=2/3`
And, `"AE"/"EC"=6/9=2/3`
Since, `"AD"/"DB"="AE"/"EC"`
Then, by converse of basic proportionality theorem
DE || BC
In ΔADE and ΔABC
∠A = ∠A [Common]
∠ADE = ∠B [Corresponding angles]
Then, ΔADE ~ ΔABC [By AA similarity]
`therefore"AD"/"AB"="DE"/"BC"` [Corresponding parts of similar Δ are proportional]
`rArr8/20="DE"/"BC"`
`rArr2/5="DE"/"BC"`
`"BC"=5/2" DE"`
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