The triangle lengths would be 14√2, 7√2 and 7√6.
The sides of a 45-45-90 triangle can be listed as t, t and t√2. The legs are each 14, so the hypotenuse will be 14√2.
This will also be the longest side of the 30-60-90 triangle. Its sides can be listed as t, 2t and t√3. Since the hypotenuse is the longest side, we have:
2t=14√2
Dividing both sides by 2, we have:
2t/2 = 14√2/2
t = 7√2
The remaining side will be t√3:
t = 7√2
t√3 = 7√2(√3) = 7√6