Concept: The question tests on the application of Geometry (Triangle)
Triangle BCA is similar to Triangle CDE (By AA) Angle BAC = Angle EDC and Angle BCA = Angle DCE
The ratio of sides have to be equal. So ABDE=BCCE=ACCDABDE=BCCE=ACCD, where DE is the smallest side, CE the second longest and CD is the longest.
Statement I: Sides are 6, 8, 14. Here AB / DE = 4/6 = 2/3 and BC/CE = 6/8 = 3/4. Therefore this is not possible.
Statement II: Sides are 8, 12, 16. Here AB / DE = BC/CE = AC/CD = 1/2. Therefore this is possible.
Statement III: Sides are 16, 24, 32. Here AB / DE = BC/CE = AC/CD = 1/4. Therefore this is possible.