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The length x of a rectangle is decreasin...

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 = 8cm and y = 6cm, find the rates of change of (a) the perimeter, and (b) the area of the rectangle

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To solve the problem, we need to find the rates of change of the perimeter and area of a rectangle when the length \( x \) is decreasing and the width \( y \) is increasing. ### Given: - Rate of change of length: \( \frac{dx}{dt} = -5 \) cm/min (negative because the length is decreasing) - Rate of change of width: \( \frac{dy}{dt} = 4 \) cm/min (positive because the width is increasing) - Length at the moment of interest: \( x = 8 \) cm - Width at the moment of interest: \( y = 6 \) cm ...
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