perplexus.info :: Just Math : Inequality in lengths of pentagon

Inequality in lengths of pentagon (Posted on 2019-04-26)

Let p denote the perimeter of a convex pentagon, and let d denote the sum of diagonals of this same pentagon.

Show that p < d < 2p

No Solution Yet Submitted by Danish Ahmed Khan

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part 1 of 2

| Comment 1 of 2

Nodes sequentially at ABCDE.

Repeated use of the triangle inequality:

AB + BC > AC

BC + CD > BD

CD + DE > CE

DE + AE > AD

AE + AB > BE

Summing: 2p > d

Posted by FrankM on 2019-04-27 00:12:18

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