In figure below, $XY\ ∥\ BC$. Find the length of $XY$.

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Given:

In the given figure $XY\ ∠¥\ BC$.

To do:

We have to find the length of $XY$.

Solution:

$AX = 1\ cm, BX = 3\ cm$ and $BC = 6\ cm$

In $\vartriangle AXY$ and $\vartriangle ABC$,

$\angle A = \angle A$ (Common)

$\angle AXY = \angle ABC$ ($XY||BC$, Corresponding angles)

Therefore,

$\vartriangle AXY ∠¼ \vartriangle ABC$ (By AA similarity)

Hence,

$\frac{XY}{BC} = \frac{AX}{AB}$ (Corresponding parts of similar triangles are

proportional)

$\frac{XY}{6} = \frac{1}{1+3}$ ($AB=AX+BX=(1+3)\ cm$)

$XY = \frac{6\times1}{4}$

$XY = 1.5\ cm$

The length of $XY$ is $1.5\ cm$.