Question

Prove that the sum of lengths of two diagonals of a quadrilateral is more than the semi perimeter of the quadrilateral.

Answer 1

Step by explanation :

1) The triangle ienquality assuure us that.

AB + BC > AC , BC + CD > BD , CD + AD>AC

and AD + AB > BD.

2) Adding all these given :

2AB + 2BC + 2CD + 2AD > 2AC + 2BD.

3) Dividing by 2 :

AB + BC + CD + AD > BD as required.

Hence proved....

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