Question

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

If AD = 4x − 3, AE = 8x – 7, BD = 3x – 1 and CE = 5x − 3, find the volume of x.

Answer 1

We have, DE || BC

Therefore, by basic proportionality theorem,

We have,

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

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

⇒ (4x − 3)(5x − 3) = (8x − 7)(3x − 1)

⇒ 4x(5x − 3) − 3(5x − 3) = 8x(3x − 1) − 7(3x − 1)

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

⇒ 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