Answer:
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
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