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A third ant walks around the perimeter of another rectangle sheet of paper. The dimensions of this sheet of paper are given in...Asked by HELP
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? HELP PLZZZZ
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Answered by
GPT 3.5
Let's assume the length of the rectangular sheet of paper is $l$ and the width is $w$.
The ant walks around the perimeter of the sheet of paper, which is equal to $2l + 2w$. We know that the ant travels a distance between 18 and 19 centimeters.
Since the tenths and hundredths digits are non-zero, we can assume that both $l$ and $w$ are greater than 1 centimeter.
To find the dimensions, we need to set up the inequality:
$18 < 2l + 2w < 19$
Dividing by 2, we get:
$9 < l + w < \frac{19}{2}$
Since $l$ and $w$ are greater than 1, we can start by trying the smallest possible values for $l$ and $w$ that satisfy the inequality.
Let's set $l = 2$ and $w = 2$.
$l + w = 2 + 2 = 4$, which is not within the range $9 < l + w < \frac{19}{2}$.
Let's try increasing the width to 3.
$l + w = 2 + 3 = 5$, which is still not within the range.
We can continue trying different values until we find the right dimensions.
After trying different values, we find that $l = 5.6$ centimeters and $w = 3.8$ centimeters satisfies the inequality:
$9 < 5.6 + 3.8 < \frac{19}{2}$
This means that the dimensions of the rectangular sheet of paper are approximately 5.6 cm by 3.8 cm.
The ant walks around the perimeter of the sheet of paper, which is equal to $2l + 2w$. We know that the ant travels a distance between 18 and 19 centimeters.
Since the tenths and hundredths digits are non-zero, we can assume that both $l$ and $w$ are greater than 1 centimeter.
To find the dimensions, we need to set up the inequality:
$18 < 2l + 2w < 19$
Dividing by 2, we get:
$9 < l + w < \frac{19}{2}$
Since $l$ and $w$ are greater than 1, we can start by trying the smallest possible values for $l$ and $w$ that satisfy the inequality.
Let's set $l = 2$ and $w = 2$.
$l + w = 2 + 2 = 4$, which is not within the range $9 < l + w < \frac{19}{2}$.
Let's try increasing the width to 3.
$l + w = 2 + 3 = 5$, which is still not within the range.
We can continue trying different values until we find the right dimensions.
After trying different values, we find that $l = 5.6$ centimeters and $w = 3.8$ centimeters satisfies the inequality:
$9 < 5.6 + 3.8 < \frac{19}{2}$
This means that the dimensions of the rectangular sheet of paper are approximately 5.6 cm by 3.8 cm.
Answered by
GPT 3.5
The dimensions of the rectangular sheet of paper are approximately 5.6 cm by 3.8 cm.
Answered by
GPT 3.5
The dimensions of the rectangular sheet of paper are 5.6 centimeters by 3.8 centimeters.
Answered by
GPT 3.5
Certainly!
To find the dimensions of the rectangular sheet of paper, we need to set up the inequality:
$18 < 2l + 2w < 19$
Since $l$ and $w$ are the length and width of the paper respectively, the expression $2l + 2w$ gives us the perimeter of the paper.
Dividing by 2, we get:
$9 < l + w < \frac{19}{2}$
This inequality tells us that the sum of the length and width of the paper must be between 9 and $\frac{19}{2}$.
Since the tenths and hundredths digits are non-zero, we can assume that both $l$ and $w$ are greater than 1 centimeter, as lengths and widths less than 1 would not satisfy the given conditions.
To find possible values for $l$ and $w$ that satisfy the inequality, we can start by trying the smallest possible values. Let's set $l = 2$ and $w = 2$.
The sum of the length and width is $l + w = 2 + 2 = 4$. However, this value is not within the range $9 < l + w < \frac{19}{2}$.
We can try increasing the width to 3, so $l = 2$ and $w = 3$.
The sum of the length and width is $l + w = 2 + 3 = 5$. However, this value is still not within the desired range.
We need to continue trying different values until we find the right dimensions.
After trying different values, we find that $l = 5.6$ centimeters and $w = 3.8$ centimeters satisfies the inequality:
The sum of the length and width is $l + w = 5.6 + 3.8 = 9.4$, which is within the range $9 < l + w < \frac{19}{2}$.
Therefore, the dimensions of the rectangular sheet of paper are approximately 5.6 centimeters by 3.8 centimeters.
To find the dimensions of the rectangular sheet of paper, we need to set up the inequality:
$18 < 2l + 2w < 19$
Since $l$ and $w$ are the length and width of the paper respectively, the expression $2l + 2w$ gives us the perimeter of the paper.
Dividing by 2, we get:
$9 < l + w < \frac{19}{2}$
This inequality tells us that the sum of the length and width of the paper must be between 9 and $\frac{19}{2}$.
Since the tenths and hundredths digits are non-zero, we can assume that both $l$ and $w$ are greater than 1 centimeter, as lengths and widths less than 1 would not satisfy the given conditions.
To find possible values for $l$ and $w$ that satisfy the inequality, we can start by trying the smallest possible values. Let's set $l = 2$ and $w = 2$.
The sum of the length and width is $l + w = 2 + 2 = 4$. However, this value is not within the range $9 < l + w < \frac{19}{2}$.
We can try increasing the width to 3, so $l = 2$ and $w = 3$.
The sum of the length and width is $l + w = 2 + 3 = 5$. However, this value is still not within the desired range.
We need to continue trying different values until we find the right dimensions.
After trying different values, we find that $l = 5.6$ centimeters and $w = 3.8$ centimeters satisfies the inequality:
The sum of the length and width is $l + w = 5.6 + 3.8 = 9.4$, which is within the range $9 < l + w < \frac{19}{2}$.
Therefore, the dimensions of the rectangular sheet of paper are approximately 5.6 centimeters by 3.8 centimeters.
Answered by
GPT 3.5
Apologies for any confusion caused.
To find the dimensions of the rectangular sheet of paper, we need to set up the inequality:
$18 < 2l + 2w < 19$
This inequality represents the distance traveled by the ant walking around the perimeter of the paper. Since the ant travels a distance between 18 and 19 centimeters, we can assume that $2l + 2w$ falls within this range.
Dividing the inequality by 2, we get:
$9 < l + w < \frac{19}{2}$
This means that the sum of the length and width of the paper must be between 9 and $\frac{19}{2}$.
Now, let's try to find the possible values for $l$ and $w$ that satisfy this inequality. We know that both $l$ and $w$ are greater than 1 centimeter, as the tenths and hundredths digits are non-zero.
Starting with the smallest possible values, let's assume $l = 2$ centimeters and $w = 2$ centimeters. In this case, the sum of the length and width is $l + w = 2 + 2 = 4$ centimeters. However, 4 is not within the range of 9 to $\frac{19}{2}$.
Let's try increasing the value of $w$. Assuming $l = 2$ centimeters and $w = 3$ centimeters, the sum of the length and width becomes $l + w = 2 + 3 = 5$ centimeters. However, 5 is still not within the desired range.
We need to keep trying different values. After trying different combinations, we find that $l = 5.6$ centimeters and $w = 3.8$ centimeters satisfy the inequality:
With $l = 5.6$ centimeters and $w = 3.8$ centimeters, the sum of the length and width becomes $l + w = 5.6 + 3.8 = 9.4$ centimeters, which is within the range $9 < l + w < \frac{19}{2}$.
Therefore, the dimensions of the rectangular sheet of paper are approximately 5.6 centimeters by 3.8 centimeters.
To find the dimensions of the rectangular sheet of paper, we need to set up the inequality:
$18 < 2l + 2w < 19$
This inequality represents the distance traveled by the ant walking around the perimeter of the paper. Since the ant travels a distance between 18 and 19 centimeters, we can assume that $2l + 2w$ falls within this range.
Dividing the inequality by 2, we get:
$9 < l + w < \frac{19}{2}$
This means that the sum of the length and width of the paper must be between 9 and $\frac{19}{2}$.
Now, let's try to find the possible values for $l$ and $w$ that satisfy this inequality. We know that both $l$ and $w$ are greater than 1 centimeter, as the tenths and hundredths digits are non-zero.
Starting with the smallest possible values, let's assume $l = 2$ centimeters and $w = 2$ centimeters. In this case, the sum of the length and width is $l + w = 2 + 2 = 4$ centimeters. However, 4 is not within the range of 9 to $\frac{19}{2}$.
Let's try increasing the value of $w$. Assuming $l = 2$ centimeters and $w = 3$ centimeters, the sum of the length and width becomes $l + w = 2 + 3 = 5$ centimeters. However, 5 is still not within the desired range.
We need to keep trying different values. After trying different combinations, we find that $l = 5.6$ centimeters and $w = 3.8$ centimeters satisfy the inequality:
With $l = 5.6$ centimeters and $w = 3.8$ centimeters, the sum of the length and width becomes $l + w = 5.6 + 3.8 = 9.4$ centimeters, which is within the range $9 < l + w < \frac{19}{2}$.
Therefore, the dimensions of the rectangular sheet of paper are approximately 5.6 centimeters by 3.8 centimeters.
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