 Hello and welcome to the session. In this session we discussed the following question which says, a wire is bent in the shape of a circular ring and then it is re-bent in the shape of an equilateral triangle each of whose size measures 8.8 centimeters find the diameter of the ring. Before moving on to the solution let's recall the formula for the perimeter of an equilateral triangle this is equal to 3a where this a is the length of each side of the equilateral triangle then we have the formula for the circumference of the circle this is equal to 2 pi r where r is the radius of the circle this is the key idea to be used in this question let's move on to the solution now we are given that each side of the equilateral triangle is of measure 8.8 centimeters so the perimeter of the equilateral triangle would be equal to 3 into 8.8 centimeters and this is equal to 26.4 centimeters now we take let r be the radius of the circular ring formed now in the question as it is given that the wire is bent in the shape of a circular ring then it is re-bent in the shape of an equilateral triangle so the perimeter of the equilateral triangle is equal to the circumference of the circle the perimeter of the equilateral triangle is 26.4 centimeters and this is equal to 2 pi r which is the circumference of the circle from here we get r is equal to 26.4 upon 2 into pi now we put the value for pi that is 22 upon 7 so r is equal to 26.4 upon 2 into 22 upon 7 from here we get r is equal to 26.4 into 7 upon 2 into 22 now 22 1.2 times as 26.4 so we get r is equal to 1.2 into 7 upon 2 then 2 0.6 times as 1.2 so r is equal to 0.6 into 7 which is equal to 4.2 centimeters thus we have the radius of the circular ring is equal to 4.2 centimeters and therefore the diameter of the circular ring is equal to 2 into the radius that is 4.2 centimeters and so this is equal to 8.4 centimeters is the diameter of the circular ring so 8.4 centimeters is our final answer this completes this session hope you have understood the solution for this question