Correct Answer: (c) x = 4

Explanation:

Given,

DE || BC

Applying Thales’ theorem,

3????(7???? − 4) = (5???? − 2)(3???? + 4)

21????² − 12???? = 15????² + 20???? − 6???? − 8

21????² − 12???? = 15????² + 14???? − 8

6????² − 26???? + 8 = 0

2 (3????² − 13???? + 4) = 0

3????² − 13???? + 4 = 0

3????² − 12???? − ???? + 4 = 0

3???? (???? − 4) − 1 (???? − 4) = 0

(???? − 4)(3???? − 1) = 0

???? − 4 = 0 ???????? 3???? − 1 = 0

???? − 4 ???????? ???? = 1/3

If ???? = 1/3,

7???? − 4 = −5/3 < 0; ???????? ???????? ???????????? ????????????????????????????????.

Hence, x = 4