Posted by **l** on Thursday, August 31, 2006 at 11:23pm.

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

Please help asap. Thank you! (so much)

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.

## Answer this Question

## Related Questions

- 2nd grade math - If you have a rectangle with 24 square units 3 lines down 8 ...
- math - the area of a rectangle is 100 square inches. the perimeter of the ...
- Math - The first question is this: Helen designs a rectangle with an area of 225...
- grade 3 math - 1) what is the greates perimeter of a rectangle with an area of ...
- Math ASAP - Height: 10 inches Base Perimeter: 40 inches Lateral Surface Area: ...
- Math - Find the Maximum area for the given perimeter of a rectangle. State the ...
- math - the area of a rectangle is 100 square inches.the perimeter of the ...
- area, perimeter - the perimeter of rectangle y is equal to its area. rectangle z...
- Algebra - The length of a rectangle is (x+2) inches. The width of the rectangle ...
- math - A rectangle has an area of 60 square inches and a perimeter of 38 inches...