What is the minimum perimeter possible for a rectangle with an area of 500 cm^2
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What is the minimum perimeter possible for a rectangle with an area of 500 cm^2

[From: ] [author: ] [Date: 11-06-15] [Hit: ]
= 4 * 22.3606= 89.......
The minimum is when the rectangle is square, A = s^2. Since you have the area, you know what the side length is, and therefore what the perimeter is.

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Short answer: the minimum perimeter of a rectangle with a given area is always a square. Thus, the the minimum perimeter occurs when the side length, s, of each side of the rectangle satisfies:
s^2 = 500 ==> s = √500 = 10√5.

Thus, the minimum perimeter is 4(10√5) = 40√5.

You can also show this via Calculus. If x is the length of the rectangle and y is the width, then the area of the rectangle is xy. Since the area is 500, you have:
xy = 500.

The perimeter of the rectangle is P = 2x + 2y. Solve xy = 500 for any variable you wish and find the value of that variable that minimizes the area. You'll get the same answer as above.

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Answer is 4 * sqrt 500 cm

= 4 * 22.3606 = 89.4427 cm
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