Question

In ΔABC, DE || BC so that AD = (7x – 4) cm, AE = (5x – 2) cm, DB = (3x + 4) cm and EC = 3x cm. Then, we have

Options

• x = 3

• x = 5

• x = 4

• x = 2.5

Answer 1

x = 4

Explanation:

Given DE || BC, we have `(AD)/(DB) = (AE)/(EC)` (Basic proportionality theorem).

Using the given values `(7x - 4)/(3x + 4) = (5x - 2)/(3x)`

Cross-multiply: 21x² – 12x = 15x² + 14x – 8 

⇒ 6x² – 26x + 8 = 0

 ⇒ 3x² – 13x + 4 = 0

Solve: `x = (13 ± 11)/6`

⇒ x = 4 or x = `1/3`.

x = `1/3` makes AE = 5x – 2 negative, so discard. 

Hence, x = 4.