a third ant walks around the perimeter of another rectangular sheet of paper the dimension 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's assume that the length of the sheet of paper is "L" centimeters, and the width is "W" centimeters.
The perimeter of the rectangular sheet of paper is given by the formula: P = 2(L + W)
Since the ant walks around the perimeter, it covers a distance between 18 and 19 centimeters. Therefore, we can write the inequality:
18 < 2(L + W) < 19
Simplifying the inequality:
9 < L + W < 9.5
Now let's try to find one possibility for the dimensions of the sheet of paper. We can assume that the width (W) is close to its maximum, which is 9.5/2 = 4.75 centimeters.
If we choose the width (W) as 4.75 centimeters, then the length (L) can be obtained by rearranging the inequality:
9 < L + 4.75 < 9.5
4.25 < L < 4.75
So, we can choose the width (W) as 4.75 centimeters and the length (L) to be any value between 4.25 and 4.75 centimeters.
One possibility is: Length (L) = 4.5 centimeters and Width (W) = 4.75 centimeters.
Therefore, one possibility for the dimensions of the sheet of paper is a rectangle measuring 4.5 centimeters by 4.75 centimeters.
That is wrong because 4.5 needs to have a non-zero in the hundreths place too.
To determine the dimensions of the sheet of paper, we need to consider the fact that the ant walks around its perimeter.
Let's assume the length of the paper is L and the width is W.
The perimeter of a rectangle is given by the formula: P = 2L + 2W.
Since the ant travels between 18 and 19 centimeters, we can set up the following inequality: 18 < 2L + 2W < 19.
Let's work with the lower bound of the inequality: 18 < 2L + 2W.
Assuming one possibility, let's say the length is 5.00 centimeters.
Substituting the values, we get: 18 < 2(5.00) + 2W.
Simplifying, we have: 18 < 10.00 + 2W.
Moving the constant term to the other side, we have: 18 - 10.00 < 2W.
Simplifying further, we get: 8 < 2W.
Dividing both sides by 2, we obtain: 4 < W.
Since the tenths and hundredths digits need to be non-zero, we can assume W = 4.50 centimeters.
So, the possible dimensions of the rectangular sheet of paper could be 5.00 centimeters by 4.50 centimeters.
To find the dimensions of the rectangular sheet of paper, we can use the information given and solve for possible values.
Let's assume the length of the sheet of paper is 'l' centimeters and the width is 'w' centimeters.
The perimeter of a rectangle is given by the formula: P = 2(l + w).
According to the problem, the ant walks around the perimeter and travels between 18 and 19 centimeters. Therefore, we can set up the following inequality:
18 < 2(l + w) < 19
Simplifying the inequality, we get:
9 < l + w < 9.5
Now, we need to find decimal numbers expressed to the hundredth place such that their sum falls between 9 and 9.5. One possible solution is:
l = 4.50 cm
w = 4.50 cm
If we substitute these values into the perimeter formula, we can verify that the ant travels between 18 and 19 centimeters:
P = 2(l + w)
P = 2(4.50 + 4.50)
P = 2(9)
P = 18 cm
Thus, one possibility for the dimensions of the sheet of paper is 4.50 cm by 4.50 cm.