Question

The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 9 cm and the width is 7 cm, how fast is the area of the rectangle increasing?

Answer 1

76cm/s

Explanation:

Let the length = L

width = W

A = LW

`(dL)/(dt) = 7 cm/s` (the rate at which the length is changing)

`(dW)/(dt) = 3cm/s` ( the rate at which the width is changing)

`(dA)/(dt) = L((dW)/(dt) + W((dL)/(dt) )` Product Rule

`(dA)/(dt) = 9(3) + 7(7)`

`(dA)/(dt) = 27 + 49`

`(dA)/(dt) = 76 cm/s`