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Question
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.
Solution
We have, DE || BC
Therefore, by basic proportionality theorem, we have,
`"AD"/"DB"="AE"/"EC"`
`rArr2.5/3.0=3.75/"EC"`
`rArr"EC"=(3.75xx3)/2.5=(375xx3)/250`
`rArr"EC"=(15xx3)/10=45/10=4.5` cm
Now, AC = AE + EC = 3.75 + 4.5 = 8.25
∴ AC = 8.25 cm
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