The length of a rectangle is increasing at a rate of 7 cm/s

Question

The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 15 cm and the width is 11 cm, how fast is the area of the rectangle increasing?

Answer 1

In the problem they tell us that

dL/dt = 7 cm/s (rate at which the length is changing) and

dw/dt = 6 cm/s (rate at which the width is changing)

Want dA/dt (rate at which the area is changing) when L = 15 cm and w = 11 cm

Equation for area of a rectangle is:

A = L·w, so will need product rule when take the derivative.

dA/dt = L (dw/dt) + w (dL/dt)

Now just plug in all of the given numbers:

dA/dt = (15)(6) + (11)(7) = 90+77 = 167

Final answer: Area is increasing at 167 cm²/second