Let the length of the shortest piece be x cm. Then, length of the second piece and the third piece are (x + 3) cm and 2x cm respectively.
Since the three lengths are to be cut from a single piece of board of length 91 cm, x cm + (x + 3) cm + 2x cm ≤ 91 cm
⇒ 4x + 3 ≤ 91
⇒ 4x ≤ 91 – 3
⇒ 4x ≤ 88
⇒ 4x/4 ≤ 88/4
⇒ x ≤22 ........(i)
Also, the third piece is at least 5 cm longer than the second piece.
∴2x ≥ (x + 3) + 5
⇒ 2x ≥ x + 8
⇒ x ≥ 8 … (2)
From (1) and (2), we obtain
8≤ x ≤ 22
Thus, the possible length of the shortest board is greater than or equal to 8 cm but less than or equal to 22 cm.