**Solution:**

Let x be the shortest board.

Then x + 3 is the second piece and 2x is the third piece.

x + (x + 3) + 2x ≤ 91

and 2x ≥ (x + 3) + 5

x + (x + 3) + 2x≤ 91

4x + 3 ≤ 91

4x ≤ 91 – 3

4x ≤88

x ≤ 44/2

2x ≥ (x + 3) + 5

2x ≥ x + 8

x ≥ 8

i.e, 8 ≤ x < 22

Thus the possible lengths of the shortest board is at least 8cm long but not more than 22cm long.