 Hi and how are you all today? I am Priyanka and let us discuss the following question. It says the longest side of a triangle is 3 times the shortest side and the third side is 2 centimeters shorter than the longest side. If the perimeter of the triangle is at least 61 centimeters, find the minimum length of the shortest side. So let us start with our solution. We need to find the shortest side. So let the shortest side be x. Now the longest side is given to us as it is 3 times the shortest side. So it would be 3 times the shortest side that is 3x. Whereas the third side is 2 centimeters shorter than the longest side. The longest side is 3x and it is 2 centimeters shorter than it. Therefore it will be 3x minus 2 centimeters. Now the perimeter of the triangle has to be at least 61 so it can be greater than equal to 61 centimeters. Perimeter means adding all these sides. So it will be x plus 3x plus 3x minus 2 has to be greater than equal to 61 centimeters. On solving it we have 7x minus 2 is greater than equal to 61. Adding 2 on both the sides we have 7x minus 2 plus 2 is greater than equal to 61 plus 2 that is 7x is greater than equal to 63. Dividing both the sides by 7 we have 7x divided by 7 is greater than equal to 63 divided by 7. On simplifying we have the value of x that is the shortest side is greater than equal to 9. Hence the minimum length of the shortest side is 9 centimeters. So this completes the question that was given to us. I hope you enjoyed. Take care.