MathDB

Problem 5

Part of 1993 French Mathematical Olympiad

Problems(1)

maxmizing volume in tetrahedron

Source: France 1993 P5

5/12/2021
(a) Let there be two given points A,BA,B in the plane. i. Find the triangles MABMAB with the given area and the minimal perimeter. ii. Find the triangles MABMAB with a given perimeter and the maximal area. (b) In a tetrahedron of volume VV, let a,b,c,da,b,c,d be the lengths of its four edges, no three of which are coplanar, and let L=a+b+c+dL=a+b+c+d. Determine the maximum value of VL3\frac V{L^3}.
geometry3D geometrytetrahedroninequalities