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Perimeter from Double-cones (Posted on 2016-02-20) Difficulty: 3 of 5
This problem is a generalization of Hypotenuse from Cone.

An acute triangle is rotated about each of its three sides to produce three double-cones of differing volumes.
The three double-cones have volumes of 55440*pi cm^3, 47520*pi cm^3, and 36960*pi cm^3.

Determine the perimeter of the triangle.

See The Solution Submitted by Brian Smith    
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re: Solution | Comment 2 of 3 |
(In reply to Solution by Jer)

I see one mistake, you wrote "So b = 166320a/142560 = (5/6)a"  This should equal (7/6)a rather than (5/6)a.  That threw off the rest of your arithmetic.  Other than that you used the same method I devised.  


For the numbers, I just picked a 6-7-9 triangle and scaled it up a bit, so yeah there are going to be roots without deliberately choosing a Heronian triangle.

  Posted by Brian Smith on 2016-02-23 12:53:07
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