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Math Help - Related Rates: Changing Dimensions in a Rectangle

  1. #1
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    Related Rates: Changing Dimensions in a Rectangle

    I am so confused on this one. I don't know if I'm suppose to use implicit differentiation like my other problems or what.

    Problem: The length L of a rectangle is decreasing at the rate of 2cm/sec while the width W is increasing at the rate of 2cm/sec. While L= 12 cm and W= 5 cm, find the rates of change of
    a) the area
    b) the perimeter
    c) the length of a diagonal in the rectangle
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  2. #2
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    Quote Originally Posted by LShimabukuro View Post
    I am so confused on this one. I don't know if I'm suppose to use implicit differentiation like my other problems or what.

    Problem: The length L of a rectangle is decreasing at the rate of 2cm/sec while the width W is increasing at the rate of 2cm/sec. While L= 12 cm and W= 5 cm, find the rates of change of
    a) the area
    b) the perimeter
    c) the length of a diagonal in the rectangle
    a) A = LW \Rightarrow \frac{dA}{dt} = L \frac{dW}{dt} + W \frac{dL}{dt} using the product rule. Therefore \frac{dA}{dt} = (12) (2) + (5) (-2) = ....

    b) P = 2W + 2L \Rightarrow \frac{dP}{dt} = ....

    c) D = \sqrt{L^2 + W^2} \Rightarrow \frac{dD}{dt} = \frac{1}{2 \sqrt{L^2 + W^2}} \cdot \left(2L \frac{dL}{dt} + 2W \frac{dW}{dt} \right) using the chain rule. Therefore ....
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