The length and breadth of a rectangular paper were measured to be the nearest centimeter and found to be 18 cm and 12 cm respectively. Find the percentage error in its perimeter.
P = 2L + 2W = 36 + 12 = 48 cm
Since you are rounding the error for each L and W < .5 cm.
With 4 sides, the should be < 2 cm.
Now, you find the percentage.
To find the percentage error in the perimeter of the rectangular paper, we need to calculate the actual perimeter of the paper and compare it with the measured perimeter.
The formula to calculate the perimeter of a rectangle is:
Perimeter = 2 * (Length + Breadth)
Given that the length is 18 cm and the breadth is 12 cm, we can substitute these values into the formula:
Perimeter = 2 * (18 cm + 12 cm) = 2 * 30 cm = 60 cm
Now, let's calculate the measured perimeter. Since the measurements were taken to the nearest centimeter, we need to consider the possible error in each measurement. The possible error for each measurement is ±0.5 cm.
So, the maximum possible length can be 18.5 cm, and the minimum possible length can be 17.5 cm. Similarly, the maximum possible breadth can be 12.5 cm, and the minimum possible breadth can be 11.5 cm.
Using the maximum possible values, we can calculate the maximum possible perimeter:
Maximum Perimeter = 2 * (18.5 cm + 12.5 cm) = 2 * 31 cm = 62 cm
Using the minimum possible values, we can calculate the minimum possible perimeter:
Minimum Perimeter = 2 * (17.5 cm + 11.5 cm) = 2 * 29 cm = 58 cm
Now, we can calculate the percentage error in the perimeter using the formula:
Percentage Error = (|Actual Value - Measured Value| / Actual Value) * 100
For the maximum possible perimeter:
Percentage Error = (|60 cm - 62 cm| / 60 cm) * 100 = (2 cm / 60 cm) * 100 ≈ 3.33%
For the minimum possible perimeter:
Percentage Error = (|60 cm - 58 cm| / 60 cm) * 100 = (2 cm / 60 cm) * 100 ≈ 3.33%
Therefore, the percentage error in the perimeter of the rectangular paper is approximately 3.33%.