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Pythagorean Pyramid (Posted on 2004-04-26) Difficulty: 3 of 5
The pictured tetrahedron has four identical rectangular (i.e., right-angled or pythagorean) triangles as faces, with

AB=CD=p,
AC=BD=q,
AD=BC=r,
and p+q=r.

What's its volume, as a function of p, q and r?






See The Solution Submitted by Federico Kereki    
Rating: 4.1250 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution by rotation | Comment 7 of 15 |
Working with my spheres, I suddenly found out an easier solution. ABC and ABD are identical triangles that share AB. We can fix C in place and rotate ABD (leaving AB fixed) until CD=AB -- and this happens only when D and C are in the same plane as A and B. 
  Posted by e.g. on 2004-04-26 15:42:41
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