Question

A rectangle has one side of 11 cm. How fast is the area of the rectangle changing at the instant when the other side is 26 cm and increasing at a rate of 3 cm per minute? Include units. At that instant, the area of the rectangle is changing at a rate of Choose one

Answer 1

Explanation:

Let's start by setting up the problem. We know that one side of the rectangle is 11 cm, and we'll call the other side x (which is increasing at a rate of 3 cm per minute). The formula for the area of a rectangle is A = l x w, where l is the length and w is the width. In this case, the length is 11 cm and the width is x. So:

A = 11x

To find how fast the area is changing, we need to take the derivative with respect to time (t):

dA/dt = 11(dx/dt)

Now we can plug in the values we know:

x = 26 cm

dx/dt = 3 cm/min

So:

dA/dt = 11(3) = 33 cm^2/min

Therefore, the area of the rectangle is changing at a rate of 33 cm^2/min at the instant when the other side is 26 cm and increasing at a rate of 3 cm per minute.