A regular tetrahedron lies with its four vertices at respective distances from the origin as 1, 2, 3 and 4 units. What is the length of each edge of the tetrahedron?

Take the 1,2,3 example, with tetrahedron side = x.

Then Area = (x^^2)(sqrt3)/4 = sqrt((x+3)/2 * (-x+3)/2 * (x+1)/2 * (x-3)/2))

which reduces to 3x^^4= (9-x^^2)(x^^2-1)

Expanding gives a quadratic in x^^2 with a negative discriminant, so there is no real solution.

Edited on March 9, 2012, 8:47 pm

Posted by xdog on 2012-03-09 20:47:17