The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 3 cm/s. when the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing? cm2/s

The rate of increase is found by differentiating with resepect to time. The product rule comes into play here.

A = LW

dA/dt ≈ (dL/dt)·W + L·(dW/dt)

... = (6 cm/s)·(5 cm) + (7 cm)·(3 cm/s)

... = 30 cm²/s + 21 cm²/s

... = 51 cm²/s . . . . rate of area increase