Question

In the figure, $DF\parallel AG,DE\parallel AB,AB=15,CD=8,AD=x,DE=10,FG=y$ and $CG=6$. The ratio $x:y$ equals to :

• A. $1:2$
• B. $1:3$
• C. $2:1$
• D. $3:2$

Answer 1

The correct option is C $2:1$

Consider $△$s $ABC,DEC$

They are similar.

$\therefore \frac{AB}{DE}=\frac{AC}{DC}=\frac{CB}{CE}$

consider,

$\therefore \frac{AB}{DE}=\frac{AC}{DC}$

$\frac{15}{10}=\frac{x+8}{8}$

$x=4$ ----------------------------------(i)

Consider $△$s $AGC,DFC$

They are similar.

$\therefore \frac{AC}{DC}=\frac{GC}{FC}=\frac{AG}{DF}$

consider,

$\therefore \frac{AC}{DC}=\frac{GC}{FC}$

$\frac{4+8}{8}=\frac{6}{FC}$

$FC=4$

From fig,

$CG=CF+FG$

$6=4+y$

$y=2$----------------------------------(ii)

Dividing (i) by (ii)

$\frac{x}{y}=\frac{4}{2}$

$\therefore x:y=2:1$