Question

In $\Delta ABC,D$ and E are points AC and BC respectively such that DE || AB. If AD = 2x, BE = 2x - 1, CD = x + 1 and CE = x - 1, then find the value of x.

Answer 1

Since, DE || AB
So, $\frac{AD}{CD}=\frac{BE}{EC}$ [By B.P.T.]
$\Rightarrow$ $\frac{2x}{x+1}=\frac{2x-1}{x-1}$
$\Rightarrow$ $2x(x-1)=(x+1)(2x-1)$
$\Rightarrow$ $2x^2-2x=2x^2+2x-x-1$
$\Rightarrow$ $-2x=x-1$
$\Rightarrow$ $1=3x$
or $x=\frac{1}{3}$