Question

The length of a rectangle is increasing at a rate of 12 in./s, while its width is decreasing at 2 in./s. Find the rate of change ofits area when its length is 25 in. and its width is 5 in.

Answer 1

In this problem, we have that

A=L*W

dL/dt=12 in/sec ----> given

dW/dt=-2 in/sec ---> given

Find out dA/dt

dA/dt=L*dW/dt+W*dL/dt

For L=25 in and W=5 in

substitute

dA/dt=25*(-2)+5*(12)

dA/dt=-50+60

dA/dt=10 in2/sec