Tomas drew a rectangular with an area of 6 square centimeters. What is the greatest possible perimeter for this rectangle

There is no "greatest" possible perimeter.

There's a smallest possible perimeter. That's a square.

Since the area is 6 square centimeters, each side of the square is

√6 = about 2.45 cm, and the perimeter is about 9.8 cm (rounded).

But there's no 'greatest' perimeter. You can take that square

and if you're careful, you can make it into rectangles that all have

the same area ... 6 square cm ... but the longer and skinnier

you make it, the greater the perimeter will be.

You can give me a number as big as you want, and I can make

a rectangle with a perimeter of your number, but an area of only

6 square centimeters!

Here are some few examples. They all have

the same area, but different perimeters:

2.45 cm by 2.45 cm ... Area = 6 square cm ... Perimeter = 9.8 cm

2 cm by 3 cm ... Area = 6 square cm ... Perimeter = 10 cm

1.5 cm by 4 cm ... Area = 6 square cm ... Perimeter = 11 cm

1.2 cm by 5 cm ... Area = 6 square cm ... Perimeter = 12.4 cm

1 cm by 6 cm ... Area = 6 square cm ... Perimeter = 14 cm

0.8 cm by 7.5 cm ... Area = 6 square cm ... Perimeter = 16.6 cm

0.6 cm by 10 cm ... Area = 6 square cm ... Perimeter = 21.2 cm

0.5 cm by 12 cm ... Area = 6 square cm ... Perimeter = 25 cm

0.4 cm by 15 cm ... Area = 6 square cm ... Perimeter = 30.8 cm

0.3 cm by 20 cm ... Area = 6 square cm ... Perimeter = 40.6 cm

0.2 cm by 30 cm ... Area = 6 square cm ... Perimeter = 60.4 cm

0.1 cm by 60 cm ... Area = 6 square cm ... Perimeter = 120.2 cm

0.001cm by 6,000cm ... Area = 6 square cm ... Perimeter = 12,000.2 cm