The length  of a rectangle is decreasing at the rate of 2 cm/sec and the width  is increasing at the rate of 2 cm/sec. When x=10 cm  and y=6 cm , find the rate of change of (i) the perimeter (ii) the area of the rectangle.

Explanation

we have


`d x / d t=-3 {cm} / {min}` and `d y / d t=2 {cm} / {mm}`


(i) The perimeter `P` of a rectangle is given by `P=2(x+y)`


Therefore `{dp} / {dt}=2({dx} / {dt}+{dy} / {dt})=2(-3+2)`


`=-2 {cm} / {min}`


(ii) The area `{A}` of the rectangle is given `{A}={x}`. `{y}`


Therefore `d A / d t=d x / d t cdot y+x . d y / d t`


`=-3(6)+10(2)(a s x=10 {cm}` and `y=6 {cm})`


...