In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = 4, AE = 8, DB = x – 4, and EC = 3x – 19, find x.
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Solution
We have,
DE || BC
Therefore, by basic proportionality theorem, we have,
`"AD"/"DB"="AE"/"EC"`
`4/(x-4)=8/(3x-19)`
⇒ 4(3x – 19) = 8(x – 4)
⇒ 12x – 76 = 8x – 32
⇒ 12x – 8x = −32 + 76
⇒ 4x = 44
⇒ 𝑥 = 44/4 = 11 cm
∴ x = 11 cm
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