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.
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Let us assume that the length and width of the rectangular sheet of paper are x and y respectively.
Since the ant walks around the perimeter of the paper, the distance it travels is equal to 2*(length + width).
Therefore, we can write the equation 2*(x+y) = 18.
However, we also know that the dimensions are given in decimal numbers expressed to the hundredth place. This means that x and y must be expressed in terms of the tenths and hundredths digits.
Let's consider one possible scenario:
If x = 8.9 cm and y = 0.1 cm, then the distance traveled by the ant would be 2*(8.9 + 0.1) = 2*9 = 18 cm.
Therefore, one possible dimension of the sheet of paper is 8.9 cm by 0.1 cm.
Let's assume the length of the rectangular sheet of paper is 'l' centimeters and the width is 'w' centimeters.
The ant walks around the perimeter of the sheet of paper, which is given by the formula: 2(l + w).
Given that the ant travels between 18 and 19 centimeters, we can write the following inequality:
18 < 2(l + w) < 19.
Dividing the inequality by 2, we have:
9 < l + w < 9.5.
Since the tenths and hundredths digits of the dimensions are non-zero, we should aim for the sum of the length and width to be as close to 9.5 as possible while still being less than 9.5.
One possibility is when l = 4.5 cm and w = 5 cm.
Let's check:
9 < l + w < 9.5,
9 < 4.5 + 5 < 9.5,
9 < 9.5 < 9.5.
Therefore, one possibility for the dimensions of the sheet of paper is 4.5 cm by 5 cm.