Let the length of the shortest piece, The length of the second price is $(x+3)$cm. The length of the third piece is 2x cm, Total length of the three prieces must be $\leq 91 cm$.

$x cm +(x+3) cm +2x cm \leq 91\;cm$

$=> 4x +3 \leq 91$

Subtracting 3 from number 4 on both sides, $ \large\frac{4x}{4} \leq \frac{88}{4}$

$x \leq 22$----(1)

Step 2:

Also third piece is at least 5 cm longer than the second piece. therefore

$2x \geq (x+3) +5$

$=> 2x \geq x+8$

Subtracting x from both sides,

$2x -x \geq 8$

$ x \geq 8$ -----(2)

Step 3:

From (1) and (2)

$8 \leq x \leq 22$

The possible length of the shortest side must be greater than or equal to 8 cm and less than or equal to 22 cm.