$ABCD$ is quadrilateral. Is $AB + BC + CD + DA < 2 (AC + BD)?$

AcademicMathematicsNCERTClass 7

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 $\Delta AOB$,  $AB$+ob$ >

In $\Delta BOC$,  $BC$+oc$ >

In $\Delta COD$,  $CD$+od$ >

In $\Delta AOD$,  $DA$+od$ >

adding  $(i)$, $(ii)$, $(iii)$ and $(iv)$

$AB+BC+CD+DA$

$AB+BC+CD+DA

$AB+BC+CD+DA

$AB+BC+CD+DA

Hence proved!
raja
Updated on 10-Oct-2022 13:34:27

Advertisements