4. A third ant walks around the perimeter of another rectangular sheet of
paper. The dimensions of this sheet of paper are given in decimal
numbers expressed to the hundredth place, with the tenths and
hundredths digits being non-zero. If the ant travels between 18 and 19
centimeters, what are the dimensions of the sheet of paper? Give one
possibility.
Let's assume one dimension of the rectangular sheet of paper is x centimeters and the other dimension is y centimeters.
When the ant walks around the perimeter of the rectangular sheet of paper, it covers a distance equal to 2x + 2y centimeters.
We are given that the ant travels between 18 and 19 centimeters, so we can write the inequality as follows:
18 < 2x + 2y < 19
Dividing the entire inequality by 2, we get:
9 < x + y < 9.5
Since x and y are decimal numbers expressed to the hundredth place, we need to find two numbers whose sum is between 9 and 9.5.
One possibility is x = 4.50 and y = 4.50. In this case, x + y = 4.50 + 4.50 = 9, which is between 9 and 9.5.
So, one possibility for the dimensions of the sheet of paper is 4.50 cm by 4.50 cm.
Let's assume the dimensions of the rectangular sheet of paper are given by length and width.
Let the length be L and the width be W.
The ant walks around the perimeter of the sheet of paper, which is equal to twice the length plus twice the width.
Perimeter = 2L + 2W
We are given that the ant travels between 18 and 19 centimeters around the perimeter.
So we can set up the following inequality:
18 ≤ 2L + 2W ≤ 19
Simplifying the inequality:
9 ≤ L + W ≤ 9.5
Since the dimensions should be in decimal numbers expressed to the hundredth place, with the tenths and hundredths digits being non-zero, we can use the following possibilities for L and W:
- L = 5.00 and W = 4.00 (giving a perimeter of 18.00 cm)
- L = 4.75 and W = 4.25 (giving a perimeter of 17.00 cm)
One possibility for the dimension could be L = 5.00 cm and W = 4.00 cm.