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.
To find the percentage error in the perimeter, we first need to calculate the actual and approximate perimeters of the rectangular paper.
The actual perimeter is given by the formula:
Perimeter = 2 × (Length + Breadth)
Plugging in the given measurements:
Actual Perimeter = 2 × (18 cm + 12 cm) = 2 × 30 cm = 60 cm
Next, we need to determine the approximate perimeter. Since the measurements were rounded to the nearest centimeter, the approximate perimeter will be calculated using the rounded values.
Approximate Perimeter = 2 × (Approximate Length + Approximate Breadth)
To determine the approximate length and breadth, we will consider the rounding error. In this case, the nearest centimeter means that the actual measurement is somewhere between 17.5 cm to 18.5 cm, and 11.5 cm to 12.5 cm for length and breadth respectively.
For the approximate length, we will use the midpoint of the possible values:
Approximate Length = (17.5 cm + 18.5 cm) / 2 = 18 cm
For the approximate breadth:
Approximate Breadth = (11.5 cm + 12.5 cm) / 2 = 12 cm
Therefore, the approximate perimeter is:
Approximate Perimeter = 2 × (18 cm + 12 cm) = 2 × 30 cm = 60 cm
Now, we can calculate the percentage error in the perimeter using the formula:
Percentage Error = [(Approximate Value - Actual Value) / Actual Value] × 100
Substituting the values:
Percentage Error = [(60 cm - 60 cm) / 60 cm] × 100 = 0%
Hence, the percentage error in the perimeter is 0%.
To find the percentage error in the perimeter, we first need to calculate the actual perimeter and the measured perimeter, and then use the formula to calculate the percentage error.
Step 1: Calculate the actual perimeter:
The actual perimeter of a rectangle is given by the formula:
Perimeter = 2 (Length + Breadth)
Given that the length is 18 cm and the breadth is 12 cm, we can calculate the actual perimeter as follows:
Perimeter = 2 (18 + 12)
Perimeter = 2 (30)
Perimeter = 60 cm
Step 2: Calculate the measured perimeter:
The measured perimeter is the sum of all sides of the rectangle, which is obtained by multiplying the measured length and measured breadth by 2.
Given that the measured length is 18 cm and the measured breadth is 12 cm, we can calculate the measured perimeter as follows:
Measured perimeter = 2 (measured length + measured breadth)
Measured perimeter = 2 (18 + 12)
Measured perimeter = 2 (30)
Measured perimeter = 60 cm
Step 3: Calculate the percentage error:
The percentage error can be calculated using the following formula:
Percentage Error = (|Measured Value - Actual Value| / Actual Value) * 100
Given that the actual perimeter is 60 cm and the measured perimeter is also 60 cm, we can calculate the percentage error as follows:
Percentage Error = (|60 - 60| / 60) * 100
Percentage Error = (0 / 60) * 100
Percentage Error = 0
Therefore, the percentage error in the perimeter is 0%.