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

Explanation

(i) perimeter = `2(x+y)`

`(dp)/(dt) = 2(dx)/(ct) + 2 (dy)/(dt)`

`= -2 xx 5 + 2 xx 4`

`= -2 (cm)/min`

(ii) `A=xy`

`(d(v v))/dx) = v(dv)/(dx) + v(dv)/(dx)`

`(dA)/(dt) = x (dy)/(dt) + y(dx)/(dt)`

`8 xx 4 + 6 xx (-5) = 32 -30 = 2 (cm^2)/min`

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