The diagonal of a square is changing at the rate of 0.5 ~cm / sec . Then the rate of change of area when the area is 400 ~cm ^2 is equal to

Step-by-step solution

array ll & d x dt =0.5 ~cm / sec & Area = x^2 2 & dA dt = 2 x 2 d x dt =x d x dt = 1 2 x array aligned [ dA dt ]_ A =400 & = 1 2 800 [ array l A =400 ~cm ^2 x= 800 ~cm array ] & =10 2 ~cm ^2 / sec aligned