Question

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

Answer 1

Since the diagonals of a trapezium divide each other proportionally.

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

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

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

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

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

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

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

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