Question

In a $\Delta ABC,DE||BC,$ if AD =x, DB = X- 2, AE = x + 2 and EC - X - 1, then value of x is

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

The correct option is C 4

In $\Delta ADEand\Delta ABC,\angle Aiscommon,\angle ADE=\angle ABCand\angle AED=\angle ACB\left[correspondinganglepairs\right]$

Hence the triangles are similar by AAA.

So, $\frac{AD}{AB}=\frac{AE}{AC}⟹\frac{x}{2x-2}=\frac{x+2}{2x+1}⟹\frac{x}{2x-2}=\frac{x+2}{2x+1}⟹2x^2+x=2x^2+4x-2x-4⟹x=2x-4orx=4$