The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 15 cm and the width is 12 cm, how fast is the area of the rectangle increasing?

105 cm ^ 2 / s

Step-by-step explanation:

We have that the area of a rectangle is given by the following equation:

A = l * w

being the length and w the width, if we derive with respect to time we have:

dA / dt = dl / dt * w + dw / dt * l

We all know these data, l = 15; w = 12; dl / dt = 5; dw / dt = 3, replacing we have:

dA / dt = 5 * 12 + 3 * 15

dA / dt = 105

Which means that the area of the rectangle increases by 105 cm ^ 2 / s