Question

In given figure, AB||DC. Find the value of x.

Answer 1

Since the diagonals of trapezium divide each other proportionally.

$\therefore$ $\frac{AO}{OC}=\frac{BO}{OD}$

$\Rightarrow$ $\frac{3x-19}{x-5}=\frac{x-3}{3}$

$\Rightarrow$ $3(3x-19)=(x-5)(x-3)$

$\Rightarrow$ $9x-57=x^2-8x+15$

$\Rightarrow$ $x^2-17x+72=0$

$\Rightarrow$ $(x-8)(x-9)=0$

$\Rightarrow$ $x-8=0$ or $x-9=0$

$\Rightarrow x=8$ or $x=9$