# The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of

3 answers

###### Question:

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 6 cm/s. when the length is 13 cm and the width is 5 cm, how fast is the area of the rectangle increasing?

## Answers

L(t) = 13 + 8t ............(1)

W(t) = 5 + 6t .............(2)

Let the area be A.

A(t) = (13 + 8t)(5 + 6t) ...(3)

Expanding the brackets in (3), we get:

[tex]A(t)=48t^{2}+118t+65\ ..........(4)[/tex]

Differentiating A with respect to time gives:

[tex]\frac{dA}{dt}=96t+118[/tex]

When t = 0, the rate of change of the area of the rectangle is: [tex]\frac{dA}{dt}=118[/tex]

Therefore the answer is 118 square cm per second.

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step-by-step explanation:

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