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13 December, 08:50

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?

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  1. 13 December, 10:42
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    150 cm/s

    Step-by-step 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
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