Question

prove that the perimeter of a quadrilateral is greater than twice of any one diagonal ​

Answer 1

Step-by-step explanation:

Prove that the perimeter of any quadrilateral is greater than twice the length of any of its diagonal.

My try: ........

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For any quadrilateral ABCD, we can easily prove that

AB+BC+CD+DA>AC+BD......(1)

Now, three cases arise. Either,

AC=BDorAC>BDorAC<BD

.

If AC=BD,then the result follows from (1).

If AC>BD⟹AC+BD>2BD and then the result follows from (1).

If BD>AC⟹AC+BD>2AC and then the result follows from (1).

I think here is ur answer

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