Question

In the below figure, If AB || CD, find the value of x.

Answer 1

`rArr(3x-1)/(5x-3)=(2x+1)/(6x-5)`

⇒ (3x – 1) (6x – 5) = (2x + 1) (5x – 3)

⇒ 3x (6x – 5) – 1(6x – 5) = 2x (5x – 3) + 1 (5x – 3)

⇒ 18𝑥² − 15𝑥 − 6𝑥 + 5 = 10𝑥² − 6𝑥 + 5𝑥 − 3

⇒ 8𝑥² − 20𝑥 + 8 = 0

⇒ 4(2𝑥² − 5𝑥 + 2) = 0

⇒ 2𝑥² − 4𝑥 − 1𝑥 + 2 = 0

⇒ 2𝑥(𝑥 − 2) − 1(𝑥 − 2) = 0

⇒ (2𝑥 − 1)(𝑥 − 2) = 0

⇒ 2x – 1 = 0 or x – 2 = 0

⇒ 𝑥 = `1/2` or 𝑥 = 2

𝑥 = `1/2` is not possible, because, OC = 5x – 3

= `5(1/2) - 3`

= `(5-6)/2`

= `-1/2`