There are two ways to approach the problem:
1. Calculate the side lengths, a,b and c.
ab=28....(1)
ac=20....(2)
bc=70....(3)
Therefore by dividing ac by bc, we get
a/b=2/7
substitute a=2b/7 into equation (1) gives 2b/7*b=28 => b²=98 => 7√2
You can calculate similarly the other sides.
2.
You are looking for the product abc, from which ab=28
So
abc=ab*bc*√((a/b)/ab)
All the products are known, the quotient has been calculated in part 1.
So the volume abc can be calculated directly.
