math
posted by l .
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.
Respond to this Question
Similar Questions

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) … 
2nd grade math
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. … 
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. … 
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? 
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. 
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? 
Math
There's a triangle the numbers on each sides are 22 25 and 11 What is it's perimeter and area? 
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 wholenumber side lengths that can be made from the perimeter of the rectangle. … 
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? 
grade 3 math
1) what is the greates perimeter of a rectangle with an area of 39 square feet?