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प्रश्न
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
बेरीज
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उत्तर १
We have,
DE || BC
Therefore, by basic proportionally theorem,
We have
`"AD"/"DB"="AE"/"EC"`
`rArr6/9=8/"EC"`
`rArr2/3=8/"EC"`
`rArr"EC"=(8xx3)/2`
⇒ EC = 12 cm
⇒ Now, AC = AE + EC = 8 + 12 = 20 cm
∴ AC = 20 cm
shaalaa.com
उत्तर २
Apply Basic Proportionality Theorem
`(AD)/(AB) = (AE)/(AC)`
`6/15 = 8/(AC)`
`6/15 = 8/(AC) => 6xxAC = 15xx8 => 6xxAC = 120 => AC = 120/6 = 20 cm`
AC = 20 cm
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