$\begin{array}{1 1} (A)\;9\;cm \\(B)\;3\;cm \\(C)\;5\;cm \\(D)\;5\;cm \end{array} $

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- Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
- Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
- If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .

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.

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