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.