What is the largest perimeter for an area of 48 cm square?

Answer 1

There is no maximum perimeter. Example: take a rectangle with area 48 cm².

Let's use (6 cm) x (8 cm) = 48 cm². Perimeter = 2*(6 cm + 8 cm) = 28 cm.

Another one: (1 cm) x (48 cm). Same area. Perimeter = 2*(1 cm + 48 cm) = 98 cm

You can keep extending the long side, and shortening the short side, and the

perimeter will approach infinity. One more example (0.1 cm) x (480 cm) = 48 cm².

Perimeter = 2*(0.1 cm + 480 cm) = 960.2 cm.

By the way: the shape with the minimum perimeteris a circle. Perimeter

(or circumference in this case) is 24.56 cm.

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Another contributor added:

Everything S.D. said is true and correct, he said it beautifully, and he be da man.

But I worked so long on this, while he was tossing it off, that I crave, with his

permission, for my work to be allowed to bask in some of his radiance:

The smallest possible perimeter for an area of 48 cm2 is 24.56 cm in a circle,

or 27.71 cm in a square.

But there's no largest perimeter. You can make it as large as you want, and

someone else can always come along and make it larger.

Here are some rectangles and their perimeters.

These all have areas of 48:

8 x 6 .. . . . . 28

10 x 4.8 . . . 29.6

12 x 4 . . . . . 32

16 x 3 . . . . . 38

24 x 2 . . . . . 52

32 x 1.5 . . . . 67

36 x 11/3 . . . 742/3

72 x 2/3 . . . . 1451/3

144 x 1/3 . . . 2882/3

192 x 0.25 . . 384.5

240 x 0.2 . . . 480.4

480 x 0.1 . . . 960.2

960 x 0.05 . . 1,920.1

.

.

etc.