# math

posted by .

Suppose the area of a rectangle is 36 square inches. Find the Minimum perimeter for a rectangle with this area.

We know that A=l*w=36 and P=2(l+w)
From the area formula we see that l=36/w
Putting this into the perimeter formula we get
P=2(36/w + w) = 72/w +2w
dP/dw= -72/w^2 +2
Set that =0 and we get -144/w^2 +2=0
2 = 72/w^2, or w^2 = 36, thus w=6 and l=6 too.
I think you should be able to prove this for the general case too.

## Similar Questions

1. ### Math

Find the Maximum area for the given perimeter of a rectangle. State the length and width of the rectangle. 28 inches Well, finally a calculus problem. Ok, we know that the area for a rectangle is A=l*w and the perimeter is P=2(l+w) …

If you have a rectangle with 24 square units 3 lines down 8 across how can you have a 4 unit rectangle with a perimeter of 8 around the outside also 6 units with a perimeter of 10 in a seprate problem A square of 4, perimeter of 8. …
3. ### math

one of the two numbers that can be both the perimeter and the area of the same rectangle I am assuming that you are seeking the two rectangles that have the area equal to the perimeter. A 4 x 4 square has a perimeter and area of 16. …
4. ### math

the area of a rectangle is 100 square inches.the perimeter of the rectangle is 40 inches.a second rectangle has the same area but a different perimeter. is the second rectangle a square?
5. ### area, perimeter

the perimeter of rectangle y is equal to its area. rectangle z has the same perimeter as rectangle y. the length of rectangle z is 5 inches and the width is 3 inches. explain how you can find the length and eidth of rectangle y.
6. ### math

the area of a rectangle is 100 square inches. the perimeter of the rectangle is 40 inches. a second rectangle has the same area but a different perimeter. is the second rectangle a square?
7. ### Math

There's a triangle the numbers on each sides are 22 25 and 11 What is it's perimeter and area?
8. ### Math

The first question is this: Helen designs a rectangle with an area of 225 square units. Her rectangle is the largest rectangle (that is, with largest area) with whole-number side lengths that can be made from the perimeter of the rectangle. …
9. ### Math ASAP

Height: 10 inches Base Perimeter: 40 inches Lateral Surface Area: 400 square inches (^^^this is the total surface area of the sides) What is the Surface Area of the triangular prism?