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$ABCD$ is quadrilateral. Is $AB + BC + CD + DA < 2 (AC + BD)?$
Given: $ABCD$ is quadrilateral.
To do: To find whether $AB + BC + CD + DA
Solution:
The sum of the length of any two sides in a triangle should be greater than the length of the third side.
In $\Delta AOB$, $AB$
In $\Delta BOC$, $BC$
In $\Delta COD$, $CD$
In $\Delta AOD$, $DA$
adding $(i)$, $(ii)$, $(iii)$ and $(iv)$
$AB+BC+CD+DA$
$AB+BC+CD+DA
$AB+BC+CD+DA
$AB+BC+CD+DA
Hence proved!
Updated on: 10-Oct-2022
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