The length of x of a rectangle is decreasing at the rate of `3cms^(-1)` and the widty `y` is increasing at the rate of `3cms^(-1)` when `x=10cm` and `y=6cm` then the rate of change of the area of rectangle is

Options

A. `10cm^(2)s^(-1)`
B. `11cm^(2)s^(-1)`
C. `12cm^(2)s^(-1)`
D. `3cm^(2)s^(-1)`

Answer

C

Explanation

Given `x=10, y=6 (dx)/(dt)=-3` and `(dy)/(dt)=3`
`:.A=xyimplies(dA)/(dt)=x(dy)/(dt)+y(dx)/(dt)`
`=10(3)+6(-3)=30-18=12cm^(2)s^(-1)`