I cut off one corner of an empty box to form an open 'pocket', so that each of the length a, breadth b, and depth c, of the initial corner was a different whole number of centimetres, and the area of each face of the 'pocket' was also an integer.
What is the area of the open 4th side of the 'pocket', in terms of a,b, and c?
(In reply to
what is wanted? by Charlie)
I noted some instances where the a, b and c were not all distinct. I've now also counted only those instances where the 4th side also has integer area:
1 2 8 9.0000000000 11
2 4 6 14.0000000000 12
2 6 8 26.0000000000 16
2 8 10 42.0000000000 20
4 6 10 38.0000000000 20
2 3 16 29.0000000000 21
2 4 16 36.0000000000 22
6 8 9 51.0000000000 23
2 10 12 62.0000000000 24
4 8 12 56.0000000000 24
3 8 14 61.0000000000 25
4 7 16 66.0000000000 27
5 8 14 69.0000000000 27
2 12 14 86.0000000000 28
4 6 18 66.0000000000 28
4 10 14 78.0000000000 28
6 8 14 74.0000000000 28
8 10 11 81.0000000000 29
2 14 16 114.0000000000 32
4 12 16 104.0000000000 32
6 10 16 98.0000000000 32
3 6 24 81.0000000000 33
2 9 24 111.0000000000 35
6 13 16 121.0000000000 35
2 16 18 146.0000000000 36
4 14 18 134.0000000000 36
6 12 18 126.0000000000 36
8 10 18 122.0000000000 36
1 4 32 66.0000000000 37
1 8 30 121.0000000000 39
11 12 16 146.0000000000 39
2 18 20 182.0000000000 40
4 16 20 168.0000000000 40
6 14 20 158.0000000000 40
8 12 20 152.0000000000 40
7 8 26 141.0000000000 41
4 6 32 116.0000000000 42
8 10 25 165.0000000000 43
2 6 36 114.0000000000 44
2 20 22 222.0000000000 44
4 8 32 144.0000000000 44
4 18 22 206.0000000000 44
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Posted by Charlie
on 2014-08-14 16:41:17 |
re: what is wanted?
