Question

Find the dimensions of a rectangle with area 1,000 m^2 whose perimeter is as small as possible. ( need to know the smaller value and larger value)

Answer 1

Let x and y be the dimensions. Then the perimeter is 2x+2y, and the area is xy = 1000.

To minimize the perimeter, set y = 1000/x and obtain the perimeter in terms of x alone,

2x + 2000/x.

To minimize this, differentiate it, to get

2 - 2000/x^2

and set this equal to zero. You get x = sqrt(1000), so y=1000/sqrt(1000)=sqrt(1000) as well, so the rectangle is actually a square.

Note: to confirm that x=sqrt(1000) is a minimizer, not a maximizer, you can compute the second derivative, which is 4000/x^3, and see that it's positive, so this critical point is a minimizer.

Answer 2

hope this helps

Answer 3

thank you so much! i started to do that and then got lost.

Answer 4

your welcome