Question

How do you find the length and width of a rectangle whose area is 900 square meters and whose perimeter is a minimum?

Answer 1

Length = Width = 30 meters

Explanation:

If `LxxW = 900`
`rArr L= 900/W`

`P = 2*(L+W)`

`color(white)("XX")` `= 2(900/W +W)`

`color(white)("XX")` `=1800W^(-1) + 2W`

The minimum will occur when `(dP)/(dW) =0`

`(dP)/(dW) = -1800W^(-2) +2 = 0`

`color(white)("XXXX")`1/W^2 = (-2)/(-1800)#

`color(white)("XXXX")` `W^2 = 900`

`color(white)("XXXX")` `W =30`

and since `LxxW =900`
`rArr L =30`