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Question
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y is increasing at the rate of 4 cm/minute. When x = 8 cm and y = 6 cm, find the rates of change of the perimeter.
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Solution
Let any instant of time t, the length of rectangle be x, the breadth be y, the perimeter be P and the area be A.
P = 2 (x + y) ....(i)
We have
`dx/dt - 5` cm/min and `dy/dt = 4` cm/min
Differentiating (i) w.r.t.x, we get,
`(dP)/dt = 2 (dx/dt + dy/dt)`
= 2 (-5 + 4)
= -2 cm / min
∴ Perimeter of the rectangle is decreasing at a rate of 2 cm/min
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