The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 15 cm and the width is 12 cm, how fast is the area of the rectangle increasing

The area of the rectangle is increasing at a rate of 168 square centimeters per second.

Step-by-step explanation:

Geometrically speaking, the area of a rectangle (), in square centimeters, is described by following expression:

(1)

Where:

- Width, in centimeters.

- Height, in centimeters.

By Differential Calculus, we find an expression for the rate of change of the area of the rectangle (), in square centimeters per second:

(2)

Where:

- Rate of change of the width of the rectangle, in centimeters per second.

- Rate of change of the length of the rectangle, in centimeters per second.

If we know that , , and , then the rate of change of the area of the rectangle is:

The area of the rectangle is increasing at a rate of 168 square centimeters per second.

(8,1)

Step-by-step explanation:

see the steps from the pic