Respuesta :
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.
[tex]P=2(l+w)[/tex]DIfferentiate the perimeter with respect to t:
[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})[/tex]From the given information:
[tex]\begin{gathered} \frac{dP}{dt}=2(3-9) \\ =2(-6) \\ =-12 \end{gathered}[/tex]Thus, the perimeter of the rectangle is decreasing at the rate of 12 inches per second.
