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In figure below, $XY\ ∥\ BC$. Find the length of $XY$.
"
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,
$\vartriangle AXY ∼ \vartriangle ABC$ (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 $1.5\ cm$.
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