In △ ABC, DE || AB, where D and E are the points on sides AC and BC , respectively ,If AD =x - 3, AC = 2x, BE = x - 2 and BC = 2x + 3 , then what is the value of x?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 9
Given :
DE || AB, where D and E are the points on sides AC and BC
AD = x - 3, AC = 2x, BE = x - 2 and BC = 2x + 3
Calculations :
In ΔABC, we have
⇒ CD = 2x - x + 3 = x + 3
⇒ EC = 2x + 3 - x + 2 = x + 5
⇒ CD/AC = EC/BC
⇒ (x + 3)/(2x) = (x + 5)/(2x + 3)
⇒ (2x + 3)(x + 3) = (x + 5)2x
⇒ 2x2 + 6x + 3x + 9 = 2x2 + 10x
⇒ 10x - 9x = 9
⇒ x = 9 cm