question_answer 7)

The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at 4 cm/minute. When x = 8 cm and y = 6 cm, find the rate of change of (a) the perimeter, and (b) the area of the rectangle. 

Answer:

Let P and A be the perimeter and area of the rectangle respectively.       Given :       = + 4 cm/minute                  ?.(1)    (a)   P = 2x + 2y (b)   = 2(?5) + 2(4) [Uasing (1)]        Perimeter of the rectangle decrease at 2 cm/minute.       (b) A = xy             = x (+ 4)+ y (?5)      [Using (1)]       = + 4x ? 5y.             Hence ara of the rectangle increase at 2cm2/minute.