Answer :

(a) It is given that the length (x) is decreasing at the rate of 5 cm/minute and the width (y) is increasing at the rate of 4 cm/minute, then we have,


The perimeter (P) of a rectangle is given by:


P = 2( x + y )



= 2(-5 +4) = -2 cm/min


Therefore, the rate of change of the perimeter is -2cm/min.


(b) It is given that the length (x) is decreasing at the rate of 5 cm/minute and the width (y) is increasing at the rate of 4 cm/minute, then we have,



Now, the area (A) of the rectangle is given by


A = x × y



= -5y + 4x


So, when x = 8cm and y = 6cm, then,



Therefore, the rate of change of the area of the rectangle is 2cm2/min.


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