Mathegoras

Solid geometry › Cubes and cuboids › Edges and diagonals of cuboids

Edge length of a cube from distances

High school · ●●●○○ 50 pts

Let PP be a point inside the cube ABCD-EFGHABCD\text{-}EFGH, where ABCDABCD and EFGHEFGH are opposite faces and E,F,G,HE,F,G,H lie directly above A,B,C,DA,B,C,D respectively. Given PA=PB=332PA=PB=\frac{3\sqrt{3}}{2} and PF=PC=1072PF=PC=\frac{\sqrt{107}}{2}, find the edge length of the cube.

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distance in 3Dcoordinate geometryperpendicular bisector