 Hello and welcome to the session. Let us understand the following question which says the length x of a rectangle is decreasing at the rate of 5 centimeter per minute and with y is increasing at the rate of 4 centimeter per minute. When x is equal to 8 centimeter and y is equal to 6 centimeter, find the rates of change of A the parameter and B the area of the rectangle. Now let's proceed with the solution. It is given to us that length x of a rectangle is decreasing at the rate of 5 centimeter per minute. That is dx by dt is equal to minus 5, negative sign because length x is decreasing and it is also given to us that with y is increasing at the rate of 4 centimeter per minute. That is dy by dt is equal to 4. Let P denotes the parameter of the rectangle. A denotes the area of the rectangle. Parameter of the rectangle is given by twice of length plus breadth. Here length is equal to x and breadth is equal to y. Therefore it is equal to twice of x plus y. Now differentiating with respect to t we get dP by dt is equal to twice of dx by dt plus dy by dt. Substituting the values of dx by dt and dy by dt we get 2 multiplied by minus 5 plus 4 which is equal to minus 2. Therefore dP by dt is equal to minus 2 centimeter per minute. This minus sign denotes that parameter for rectangle is decreasing at the rate of minus 2 centimeter per minute. Now area of a rectangle is given by x multiplied by y where x is length and y is breadth of the rectangle. Now differentiating with respect to t we get dA by dt is equal to x multiplied by dy by dt plus y multiplied by dx by dt using the product rule which is equal to x and y are given to us as 8 centimeter and 6 centimeter. This is equal to 8 multiplied by dy by dt is equal to 4 plus y is equal to 6 multiplied by dx by dt is equal to minus 5. It is equal to 8 4 or 32 plus 6 multiplied by minus 5 is equal to minus 30 which is equal to 32 minus 30 is equal to 2. Therefore dA by dt is equal to 2 centimeter per minute. The meter of a rectangle is decreasing at the rate of minus 2 centimeter per minute and area of a rectangle is increasing at the rate of 2 centimeter per square per minute. I hope you understood this question. Bye and have a nice day.