Question

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. when the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

Answer 1

L(t) = 13 + 8t ............(1)
W(t) = 5 + 6t .............(2)
Let the area be A.
A(t) = (13 + 8t)(5 + 6t) ...(3)
Expanding the brackets in (3), we get:
$A(t)=48t^{2}+118t+65\ ..........(4)$
Differentiating A with respect to time gives:
 $\frac{dA}{dt}=96t+118$
When t = 0, the rate of change of the area of the rectangle is: $\frac{dA}{dt}=118$
Therefore the answer is 118 square cm per second.