Solved: The length \(x\) of a rectangle is decreasing at the rate of \(5,\text{cm/min}\)...

Q: The length \(x\) of a rectangle is decreasing at the rate of \(5,\text{cm/min}\), and the width \(y\) is increasing at the rate of \(4,\text{cm/min}\). When \(x = 8,\text{cm}\) and \(y = 6,\text{cm}\), find the rate of change of:(a) Perimeter (b) Area

Explanation: (a) Perimeter: The perimeter is \(P = 2(x + y)\) \[\frac{dP}{dt} = 2\left(\frac{dx}{dt} + \frac{dy}{dt}\right) = 2(-5 + 4) = -2,\text{cm/min}\] (b) Area: The area is \(A = xy\) \[\frac{dA}{dt} = \frac{dx}{dt} \cdot y + x \cdot \frac{dy}{dt} = (-5)(6) + (8)(4) = -30 + 32 = 2,\text{cm}^2/\text{min}\]

Class: 12 Subject: Math Topic: Application of Derivative

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The length \(x\) of a rectangle is decreasing at the rate of \(5,\text{cm/min}\), and the width \(y\) is increasing at the rate of \(4,\text{cm/min}\). When \(x = 8,\text{cm}\) and \(y = 6,\text{cm}\), find the rate of change of:(a) Perimeter (b) Area

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