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.
What measurement is given for the perimeter?
To find the percentage error in the perimeter of the rectangular paper, we need to compare the actual perimeter with the measured perimeter.
Given that the length and breadth of the paper were measured to the nearest centimeter, we can consider the actual length to be any value between 17.5 cm and 18.5 cm, and the actual breadth to be any value between 11.5 cm and 12.5 cm.
Let's calculate the actual perimeter of the rectangular paper:
Actual perimeter = 2 × (Actual length + Actual breadth)
Considering the minimum values of the length and breadth, we have:
Actual perimeter = 2 × (17.5 cm + 11.5 cm) = 2 × 29 cm = 58 cm
Now, let's calculate the measured perimeter of the rectangular paper:
Measured perimeter = 2 × (Measured length + Measured breadth)
Measured length = 18 cm
Measured breadth = 12 cm
Measured perimeter = 2 × (18 cm + 12 cm) = 2 × 30 cm = 60 cm
To find the percentage error, we'll use the formula:
Percentage error = (|Actual perimeter - Measured perimeter| / Actual perimeter) * 100
Percentage error = (|58 cm - 60 cm| / 58 cm) * 100
Percentage error = (|-2 cm| / 58 cm) * 100
Percentage error = (2 cm / 58 cm) * 100
Percentage error = (0.0345) * 100
Percentage error ≈ 3.45%
Therefore, the percentage error in the perimeter of the rectangular paper is approximately 3.45%.