He length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

The area of the rectangle increases are the rate of 132 cm²/s when the length is 13 cm and the width is 5 cm

Step-by-step explanation:

The area of the rectange is given by the following formula:

In which A is the area, measured in cm², l is the lenght and w is the width, both measured in cm.

The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 9 cm/s.

This means that

When the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

We have to find when

Applying implicit differentitiation:

We have three variables(A, l, w). So

The area of the rectangle increases are the rate of 132 cm²/s when the length is 13 cm and the width is 5 cm