Question

In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC

If AD = 8x − 7, DB = 5x − 3, AE = 4x − 3 and EC = (3x − 1), find the value of x.

Answer 1

We have,

DE || BC

Therefore, by basic proportionality theorem, we have,

`"AD"/"DB"="AE"/"EC"`

`rArr(8x-7)/(5x-3)=(4x-3)/(3x-1)`

⇒ (8x − 7)(3x − 1) = (4x − 3)(5x − 3)

⇒ 24x² − 8x − 21x + 7 = 20x² − 12x − 15x + 9

⇒ 24x² − 20x² − 29x + 27x + 7 − 9 = 0

⇒ 4x2 − 2x − 2 = 0

⇒ 2[2x² − x − 1] = 0

⇒ 2x² − x − 1 = 0

⇒ 2x² − 2x + 1x − 1 = 0

⇒ 2x(x − 1) + 1(x − 1) = 0

⇒ (2x + 1) (x – 1) = 0

⇒ 2x + 1 = 0 or x – 1 = 0

⇒ x = −1/2 or x = 1

𝑥 = −1/2 is not possible

∴ x = 1