### Home > APCALC > Chapter 8 > Lesson 8.3.2 > Problem8-114

8-114.

The length of a rectangle is increasing at a rate of $6$ cm/sec and its width is increasing at a rate of $2$ cm/sec. When the length is $30$ cm and the width is $15$ cm, how fast is the area of the rectangle increasing?

$A = lw$

Implicitly differentiate the area function with respect to time.

$\frac{dA}{dt}=\frac{dl}{dt}(w)+(l)\frac{dw}{dt}$

$\frac{dA}{dt}=(6\text{ cm/sec})(15\text{ cm}) + (30\text{ cm})(2\text{ cm/sec})$