Answer :

Let us assume the length of the shortest piece be x cm

∴ According to the question, length of the second piece = (x + 3) cm

And, length of third piece = 2x cm

As all the three lengths are to be cut from a single piece of board having a length of 91 cm

∴ x + (x + 3) + 2x ≤ 91 cm

= 4x + 3 ≤ 91

= 4x ≤ 88

= x ≤ 22 …(i)

Also, it is given in the question that, the third piece is at least 5 cm longer than the second piece

∴ 2x ≥ (x+3) + 5

2x ≥ x + 8

x ≥ 8 …(ii)

Thus, from equation (i) and (ii) we have:

8 ≤ x ≥ 22

Hence, it is clear that the length of the shortest board is greater than or equal to 8 cm and less than or equal to 22 cm

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