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Math Help - Area of rectangle

  1. #1
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    Area of rectangle

    If a rectangle has a base of 2cm, and length of 3cm, and its base increases by 1cm/s and its length increases by 2cm/s, at what rate is the area increasing when the area is 28cm^2?

    Is the answer to this 15cm^2/s?
    Last edited by BrownianMan; March 4th 2010 at 02:42 PM.
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  2. #2
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    Ok

    Think of the graph of time on x axis and length on y axis plot the lines of length and base:

    (y=mx+c where c is value when t=0 and m is the rate of change of length)

    Length y = 2+x
    Base y= 3+2x

    So

    Area = (2+x)(3+2x)

    solve 28=(2+x)(3+2x) to give 2 values for time when area=28.

    One of these values are negative, and this clearly is invalid as you can't have negative time.

    ---------------------------------------------------------------------

    Now the area at any point in time is (2+x)(3+2x) as shown above.

    Put this equal to y and find "dy by dx"

    Put your realistic value for time in here to get the rate of change of area at this point

    It comes out at 15cm^2/s

    EDIT:Aha i didn't read your post properly - you just wanted confirmation - well yea its 15 - sorry
    Last edited by Bladeowen; March 4th 2010 at 04:11 PM. Reason: Aha i didn't read your post properly - you just wanted confirmation - well yea its 15 :)
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  3. #3
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    Thanks!

    This was a question on a test I just had. Glad to get confirmation of its accuracy!
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