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The length x of a rectangle is decreasing at the rate of 3 cm/

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The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When $x = 10$ cm and $y = 6$ cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.

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The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When

x = 10

cm and

y = 6

cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.

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Text solutionVerified

Solution:

\frac{d x}{d t} = - 3 c m / min, \frac{d y}{d t} = + 2 c m / min

x = 10 c m, y = 6 c m

a)perimeter

= 2 (x + y)

\frac{d 2 ( x + y )}{d t} = 2 \frac{d ( x + y )}{d t}

= 2 (\frac{d x}{d t} + \frac{d y}{d t})

= 2 (- 3 c m / min + 2 c m / min)

= - 2 c m / min

A r e a = (x y)

\frac{d a}{d t} = \frac{d x y}{d t}

= \frac{d x}{d t} . y + x \frac{d y}{d t}

= (- 3.6 + 10.2)

= 2 c m^{2} / min

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Question Text	The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When $x = 10$ cm and $y = 6$ cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.
Answer Type	Text solution:1
Upvotes	150