Question

The length of a rectangle is increasing at a rate of 6cm/s and its width is increasing at a rate of 3cm/s. When the length is 20cm and the width is 15cm, how fast is the area of the rectangle increasing?

Answer 1

150 cm/s

Explanation:

We have that the area of a rectangle is as follows:

a = l * w

they ask us to change the increase in area with respect to time, therefore, if we derive with respect to t we are left with:

da / dt = w * (dl / d) t + l * (dw / dt)

From the statement we know that:

l = 20 cm

w = 15 cm

dl / dt = 6 cm / s

dw / dt = 3 cm / s

replacing each value we have:

da / dt = 15 * 6 + 20 * 3

da / dt = 150

Which means that 150 cm / s increases the area of the rectangle in relation to time