The longest side of a triangle is three times the shortest side and third side is 2 cm shorter than the longest side if the perimeter of the triangles at least 61 cm,

Let the shortest side of the triangle be x cm.

Then, the longest side will be 3x and the third side will be 3x − 2.

$\therefore$ Perimeter of the triangle $\geq 61$

$\Rightarrow x+3 x+3 x-2>61$

$\Rightarrow 7 x \geq 61+2$

$\Rightarrow x \geq 9 \quad$ (Dividing throughout by 7$)$

Hence, the minumum length of the shortest side is $9 \mathrm{~cm}$.