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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?

 Nov 23, 2020
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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

 

 

cool cool cool

 Nov 23, 2020
edited by CPhill  Nov 23, 2020

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