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
the maximum and minimum dimensions are
18.5*12.5 and 17.5*11.5
find the difference from the true perimeter P=2(12+18) and divide it by P
To find the percentage error in the perimeter of the rectangular paper, we need to calculate the actual perimeter and compare it to the measured perimeter.
First, let's find the actual perimeter of the rectangle.
The formula for the perimeter of a rectangle is P = 2(l + b), where P is the perimeter, l is the length, and b is the breadth.
Given:
Measured length = 18 cm
Measured breadth = 12 cm
Actual length = 18 cm
Actual breadth = 12 cm
So, the actual perimeter of the rectangle is:
P_actual = 2(18 + 12)
= 2(30)
= 60 cm
Now, let's find the measured perimeter of the rectangle.
Measured perimeter = 2(l + b)
= 2(18 + 12)
= 2(30)
= 60 cm
Since the measured perimeter is the same as the actual perimeter, there is no error in this case.
To calculate the percentage error, we use the formula:
Percentage error = (|Measured Value - Actual Value| / Actual Value) * 100
In this case, the percentage error = (|60 - 60| / 60) * 100 = 0
Therefore, the percentage error in the perimeter of the rectangular paper is 0%.
To find the percentage error in the perimeter of the rectangular paper, we need to compare the actual perimeter with the measured perimeter and calculate the percentage difference.
First, let's find the actual perimeter of the rectangular paper using the given measurements:
Perimeter = 2 × (Length + Breadth)
= 2 × (18 cm + 12 cm)
= 2 × 30 cm
= 60 cm
Now, let's find the measured perimeter considering the nearest centimeter measurements:
Measured Perimeter = 2 × (Measured Length + Measured Breadth)
The nearest centimeter measurements are 18 cm and 12 cm. Since these are the actual measurements, there is no need to change them. So the measured perimeter is:
Measured Perimeter = 2 × (18 cm + 12 cm)
= 2 × 30 cm
= 60 cm
Now, let's calculate the percentage error in the perimeter:
Percentage Error = ((Actual Perimeter - Measured Perimeter) / Actual Perimeter) × 100
Percentage Error = ((60 cm - 60 cm) / 60 cm) × 100
= (0 / 60 cm) × 100
= 0%
Therefore, the percentage error in the perimeter of the rectangular paper is 0%.