Question

In the given figure , X Y $\parallel$ BC. Find the length of X Y.

Answer 1

As $XY\parallel BC$

$\angle AXY=\angle ABC$

$\angle AYX=\angle ACB$

So by $AAA$ $△AXY\sim △ABC$

Hence $\frac{AX}{AB}=\frac{XY}{BC}$

$\frac{AX}{AX+XB}=\frac{XY}{BC}$

$\frac{1}{4}=\frac{XY}{6}$

$XY=1.5cm$

So $XY=1.5cm$