Practicing Success
The length x of a rectangle is decreasing at the rate of 10 cm/minute and the width y is decreasing at the rate of 10 cm/minute. Then which of the following is true regarding the rate of change of area and the rate of change of perimeter when x=2 cm and y = 2cm. |
Both area and perimeter increase with the same speed Both area and perimeter decrease with the same speed The area increases and the perimeter decreases The area decreases and the perimeter increases |
Both area and perimeter decrease with the same speed |
A = x.y P = 2(x+y) $\frac{dA}{dt} = x\frac{dy}{dt} + y\frac{dx}{dt} = 2\times -10 + 2\times -10 = -40 cm^2/minutes$ $\frac{dP}{dt} = 2(\frac{dx}{dt} + \frac{dy}{dt}) = -40 cm/minutes$ $\Rightarrow \frac{dA}{dt} = \frac{dP}{dt}$ Both decreases at the same rate. |