Question

A rectangle has a length of 9 inches and a width of 4 inches whose sides are changing. The length is decreasing by 5 in/sec and the width is shrinking at 6 in/sec. What is the rate of change of the area?

Answer 1

The rate of change of the area of the rectangle is -74 in^2/sec.

Step-by-step explanation:

To find the rate of change of the area, we need to know how the area of the rectangle changes with respect to time.

The formula for the area of a rectangle is A = length * width.

In this case, the length is decreasing by 5 in/sec and the width is shrinking at 6 in/sec.

So, the rate of change of the area is given by:

dA/dt = (d(length)/dt) * width + length * (d(width)/dt)

Substituting the given values:

dA/dt = (-5 in/sec) * 4 in + 9 in * (-6 in/sec)

Simplifying the equation:

dA/dt = -20 in^2/sec + (-54 in^2/sec)

dA/dt = -74 in^2/sec