 Hi and welcome to the session. I am Deepika here. Let's discuss the question. The question says is it possible to design a rectangular park of perimeter 80 meter and area 400 meters square? If so, find its length and breadth. We know that perimeter of a rectangle is equal to twice length plus breadth and area of a rectangle is equal to length into breadth. So this is a key idea behind the above question. So let's start the solution. Let breadth of the rectangle is equal to x meter. Given perimeter is equal to 80, this implies twice length plus breadth is equal to 18. Now our breadth is x meter. This implies twice length plus x is equal to 80. This implies length plus x is equal to 40. This implies length is equal to 40 minus x. Now area of the rectangle is given to us 400 meters square. This implies length into breadth is equal to 400 meters square. This implies length is of 40 minus x and breadth we have assumed x meter. Therefore 40 minus x into x is equal to 400 meter square. Again this implies 40x minus x square is equal to 400. This implies x square minus 40x plus 400 is equal to 0. Now this is a quadratic equation on comparing with a x square plus b x plus c is equal to 0. We get a is equal to 1, b is equal to minus 40, c is equal to 400. Now discriminant b square minus 4ac is equal to minus 40 square minus 4 into 1 into 400 which is equal to 1600 minus 1600 which is equal to 0. Because discriminant b square minus 4ac is equal to 0, therefore the roots are equal and real. Now we will find the roots. Hence it is possible to design a rectangular park whose perimeter is 80 meter and area is 400 meter square. Now we will find the roots. Let alpha and beta be the roots of the equation. Now we know that for equal roots alpha is equal to minus b by 2a because discriminant is 0. Therefore alpha is equal to minus b by 2a and beta is also equal to minus b by 2a. Therefore alpha is equal to minus of minus 40 upon 2 into 1 and beta is equal to minus of minus 40 upon 2 into 1. Therefore alpha is equal to 20 and beta is equal to 20. Hence the length and the breadth of a rectangular park are 20 meter and 20 meter. Hence our answer is yes it is possible to design a rectangular park of perimeter 80 meter and area 400 meter square. And its length is 20 meter and breadth is also 20 meter. I hope the question is great to you. Bye and have a good day.