In the given figure, DE ∥ BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then find the value of x.  

Correct option is B

Given:

DE ∥ BC AD = x, DB = x - 2, AE = x + 2, and EC = x - 1

Formula Used:

By the basic proportionality theorem, if a line is parallel to the side of a triangle and intersects the remaining two sides into two distinct points, then the lines divide the sides into proportion.

$$\frac{AD }{DB }= \frac{AE }{EC}$$

Soluiton:

By basic proportionality:

​$$\frac{AD }{DB}= \frac{AE }{EC } \\\ \\\frac{x }{ (x - 2) }= \frac{(x + 2) }{(x - 1) } \\\ \\x(x - 1) = (x + 2)(x - 2) \\\ \\x² - x = x² + 2x - 2x - 4 \\\ \\x = 4$$​​