 Hello and welcome to the session. In this session we discussed the following question which says each side of a square field measures 20 meters adjacent to this field there is a rectangular field having its size in the ratio 1 is to 3. If the perimeters of both of the fields are equal, find the dimensions of the rectangular field. Before we move on to the solution for this question let's recall the formula to find out the perimeter of a rectangle this is equal to 2 into L plus B where this L is the length of the rectangle and B is the breadth of the rectangle. Then we have the perimeter of a square is equal to 4 into A where this A is the side of the square. This is the key idea to be used in this question. Now we move on to the solution. Consider the square field ABCD with each side measuring 20 meters so we have the side of the square field is equal to 20 meters so we have the perimeter of the square field would be equal to 4 into the side that is 4 into 20 meters which is equal to 80 meters this is the perimeter of the square field ABCD. Now we are given in the question that we have a rectangular field adjacent to the square field with sides in the ratio 1 is to 3 so we take let the length of the rectangular field be equal to x meters that is 1 into x meters so we take this PQ to be x meters and let the breadth of the rectangular field be equal to 3 x meters so the perimeter of the rectangular field will be equal to 2 into L plus B that is this would be equal to 2 into x plus 3 x meters and so this is equal to 2 into 4 x meters equal to 8 x meters this is the perimeter of the rectangular field PQRS in the question we have that the perimeters of both the fields that is the rectangular field and the square fields are equal that is the perimeter of the square field is equal to the perimeter of the rectangular field so this would be 80 is equal to 8 x now dividing both sides by 8 we get x is equal to 10 since we know that 8 10 times is 80 and this 8 cancels with this 8 so we get the value of x as 10 so the length of the rectangular field equal to x meters so as the value of x is 10 so length of the rectangular field would be equal to 10 meters now the breadth of the rectangular field is equal to 3 x meters putting the value of x as 10 we get the length of the rectangular field is equal to 3 into 10 meters which is equal to 30 meters so we have got the length of the rectangular field equal to 10 meters and the width of the rectangular field equal to 30 meters which is our final answer this completes the session hope you have understood the solution of this question