Let the length of the shortest side be $ x\;cm$
Length of the largest side is $3x\;cm$
Length of the third side is $3x-2\;cm$
Since the perimeter of the triangle is at least 61 cm, we get,
$x +3x +3x-2 \geq 61$
$=> 7x -2 \geq 61$
Adding 2 on both sides,
$=> 7x \geq 61+2$
$7x \geq 63$
Dividing both sides by positive number 7.
$\large\frac{7x}{7} \geq \frac{63}{7}$
$x \geq 9$
Step 2:
The minimum length of the shortest side is 9 cm.
Hence A is the correct answer.