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1. A rectangle of length L and width W has a constant area of 1800 in^2. The length changes at a rate of dL/dt inches per minute.
(a) Find dW/dt in terms of W and dL/dt.
(b) At a particular instant, the length is increasing a 6 in/min and the width is decreasing at 2 in/min. Find the dimensions of the rectangle at this instant.
(c) At the instant in part b, is the length of the diagonal increasing or decreasing? At what rate?

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a)
Let L = Length of the rectangle
Let W = Width of the rectangle

Since the area of the rectangle is 1800 in2, ,
LW = 1800.
-----Equation 1

Differentiate with respect to t to get
-----Equation ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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