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

Concept: Basic Proportionality Theorem Or Thales Theorem

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