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A rectangle has a length of 9 inches and a widt of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec. What is the rate of change of the perimeter?

User Hamed MP
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1 Answer

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Given:

A rectangle has a length of 9 inches and a width of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec.

To find:

The rate of change of the perimeter.

Solution:

It is known that the perimeter of the rectangle is twice the sum of length and width.


P=2(l+w)

DIfferentiate the perimeter with respect to t:


(dP)/(dt)=2((dl)/(dt)+(dw)/(dt))

From the given information:


\begin{gathered} (dP)/(dt)=2(3-9) \\ =2(-6) \\ =-12 \end{gathered}

Thus, the perimeter of the rectangle is decreasing at the rate of 12 inches per second.

User Dong Chen
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