Let triangle PQR be a triangle in the plane, and let S be a point outside the plane of triangle PQR, so that SPQR is a pyramid whose faces are all triangles. Suppose that every edge of SPQR has length 18 or 41, but no face of SPQR is equilateral. Then what is the sum of the edge lengths of SPQR?
+130511 I'm assuming a regular triangular pyramid
The sides of the triangle cannot be 18, 18 and 41 because this violates the triangular inequality
So....the sides must be 41,41 and 18 where 41 is the slant height and 18 a base edge
Sum of edge lengths = 3 ( 18 + 41) = 3 ( 59) = 177
