The length of a rectangle is decreasing at the rate of `5 cm`/`min` and the width is increasing at the rate of `4cm`/`min`. When length is `3 \ \ cm` and width is `2 \ \ cm` , find the rates of change of the perimeter and the area of the rectangle.

Explanation

(i)

It is given that length `(x)` is decreasing at the rate of `5 cm`/`min`


and the width `(y)` is increasing at the rate of `4 cm`/`min`,


`(dx)/(dt)=−5 cm`/`min` and `(dy)/(dt)=4 cm`/`min`


Thus the perimeter`(P)` of a rectangle is, `P=2(x+y)`


`(dP)/(dt)=2((dx)/(dt)+ (dy)/(dt))=2(−5+4)=−2 cm`/`min`


Hence, the perimeter is decreasing at the rate of `2 cm`/`min`.




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