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Let $XYZ$ and $RST$ be two similar triangle

then

$RSXY =RTXZ =STYZ −−−(1)$

The perimeter of $△XYZ=XY+YZ+XZ−−−(2)$

The perimeter of $△RST=RS+ST+RT−−−(3)$

from equation $(1)$

$RSXY =RTXZ =STYZ =RS+RT+STXY+XZ+YZ $

$=Perimeterof△RSTPerimeterof△XYZ $

from $(2)$ &$(3)$

$∴$ Hence proved.

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