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Question

The length of rectangle is decreasing at the rate of 5 cm / min and the width y is increasing at the rate of 4cm/min when x=8 and y=6 , find the rate of change of
(a) the perimeter and (b) the area of the rectangle?

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Solution

Length x decreasing @5 cm/min
width y increasing =4 cm/min
a) Perimeter
dydx=5 cm/min P=2(l+b)
dydt=4 cm/min =2(x+y)
dpdt=2dxdt+2dydt
=2 cm/min
b) Area of rectangle
Rate of change of area
dydt=4 cm/mindxdt=5 cm/min
A=l×b=x×y
dAdt=ddt+xdydt
=[6×(5)+8×(4)] cm2/min
=[30+32] cm2/min
=2 cm2/min

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