Question

In the following figure, $XY$ is parallel to $BC$, $AX=9cm$. $XB=4.5cm$ and $BC=18cm$. Find $XY$ in cm.

Answer 1

In $△$s AXY and ABC,

$\angle XAY=\angle BAC$ (Common angle)

$\angle AXY=\angle ABC$ (Corresponding angles for parallel lines, XY II BC)

$\angle AYX=\angle ACB$ (Corresponding angles for parallel lines, XY II BC)

Thus, $△AXY\sim △ABC$

Hence, $\frac{AX}{AB}=\frac{XY}{BC}$ (Using similar triangle property)

$\frac{AX}{AX+XB}=\frac{XY}{18}$

$\frac{9}{9+4.5}=\frac{XY}{18}$

$XY=\frac{18\times 9}{13.5}$

$XY=12$