A square plate is contracting at a uniform rate of 2 cm ^2 / min. The rate at which the perimeter is decreasing when the side of the square is 16 cm is:

Step-by-step solution

Let x be the side length of the square plate. Area of the square, A = x^2 Perimeter of the square, P = 4x Given that the area is contracting at a uniform rate of 2 cm ^2/ min , we have: dA dt = -2 Differentiating A = x^2 with respect to t : dA dt = 2x dx dt Substituting dA dt = -2 and x = 16 : -2 = 2(16) dx dt dx dt = - 1 16 cm / min Now, differentiating P = 4x with respect to t : dP dt = 4 dx dt Substituting the value of dx dt : dP dt = 4 (- 1 16 ) = - 1 4 cm / min The negative sign indicates that the perimeter is