Geodesic
On Maximal Perimeter of a Convex Pentagon with a Fixed Diameter
Matematičeskoe obrazovanie, Tome 53 (2010) no. 1, pp. 12-16.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the regular pentagon has the maximal perimeter among all of the convex pentagons with a fixed diameter. 
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     title = {On {Maximal} {Perimeter} of a {Convex} {Pentagon} with a {Fixed} {Diameter}},
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F. L. Varpakhovskii; O. Logvinenko. On Maximal Perimeter of a Convex Pentagon with a Fixed Diameter. Matematičeskoe obrazovanie, Tome 53 (2010) no. 1, pp. 12-16. http://geodesic.mathdoc.fr/item/MO_2010_53_1_a2/