Question

The length of a rectangle is increasing at a rate of 5 in. /s while its width is increasing at 3 in. /s find the rate of change of its area when its length is 45in and its width is 35in

Answer 1

Given:

length of a rectangle is increasing at a rate of 5 in. /s and width is decreasing at 3 in. /s

Let x and y are the length and width of the rectangle respectively.

`(dx)/(dt)=5\text{ in./s ; }(dy)/(dt)=-3\text{ in./s ; x=}45\text{ in. ; y=35 in.}`

Area of the rectangle (A)= length(x) X width(y)

`A=x* y`

Differentiate with respect to t

`(dA)/(dt)=\text{x}\frac{\text{dy}}{dt}+\text{y}\frac{\text{dx}}{dt}`
`(dA)/(dt)=45(-3)+35(5)`
`(dA)/(dt)=-135+175`
`(dA)/(dt)=40in^2\text{ /s}`
`\text{Rate of change of its area is 40 in}^2\text{ /s}`