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Rectangle Problem: A rectangle of length L and width W has a constant area of 1200 in.2
Chapter 4, Problem 10(choose chapter or problem)
Rectangle Problem: A rectangle of length L and width W has a constant area of \(1200 \mathrm{in.}^{2}\). 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 at 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 of the rectangle increasing or decreasing? At what rate?
Questions & Answers
QUESTION:
Rectangle Problem: A rectangle of length L and width W has a constant area of \(1200 \mathrm{in.}^{2}\). 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 at 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 of the rectangle increasing or decreasing? At what rate?
ANSWER:Step 1 of 3
a)
Write equation that relates area, length and width and differentiate with respect to time
\(\begin{aligned}
L W & =1200 \\
\frac{d L}{d t} W+L \frac{d W}{d t} & =0 \\
\frac{d W}{d t} & =\frac{-L}{W} \frac{d L}{d t} \\
\frac{d W}{d t} & =\frac{-\frac{W}{1200}}{W} \frac{d L}{d t} \\
\frac{d W}{d t} & =\frac{-W^{2}}{1200} \frac{d L}{d t}
\end{aligned}\)