Question -
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
= 4x/4 ≤ 88/4
= 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.