Question

Find the rate of change of its area when its length is 75in and its width is 35in

Answer 1

The lenght of the rectangle is increasing at the rate of 8in/sec while its width is decreasing at 3 in/sec. Find the rate of change of it's area when it's length is 75 in and width is 35in

Solution :

Let x be the length and y is the width of the rectangle

It is given that increase length of rectnagle is 8

i.e.,

`(dx)/(dt)=8`

It is given that decrease width of rectangle is 3in/sec

i.e.,

`\frac{\text{ dy}}{\text{ dt}}=-3`

Area of rectangle is defined as the product of length and breadth

`\text{ Area = xy}`

Differentiate the area with respect to time t;

`\text{ }(dA)/(dt)\text{ = x}(dy)/(dt)+y(dx)/(dt)`

Substitute the value as x = 75 and y = 35 dx/dt = 8 and dy/dt = -3

`\begin{gathered} \text{ }(dA)/(dt)\text{ = x}(dy)/(dt)+y(dx)/(dt) \\ \text{ }(dA)/(dt)=75*(-3)+35*8 \\ \text{ }(dA)/(dt)=-225+280 \\ \text{ }(dA)/(dt)=55 \end{gathered}`

Rate of change of area is 55 unit square

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