If the length of the diagonal of a square is increasing at the rate of 0.1 ~cm / sec . What is the rate of increase of its area when the side is 15 2 ~cm ?

Step-by-step solution

Let a be the side length and d be the diagonal of the square. The relationship between the diagonal and the side is d = a 2 , which implies a = d 2 . The area A of the square is given by A = a^2 . Substituting a = d 2 , we get A = ( d 2 )^2 = d^2 2 . Differentiating both sides with respect to time t , we obtain dA dt = 1 2 2d dd dt = d dd dt . Given the side length a = 15 2 cm , the diagonal d = a 2 = ( 15 2 ) 2 = 15 cm . The rate of change of the diagonal is given as dd dt = 0.1 cm/sec . Substituting these values