Question

question 27 (3 points)
estimate the amount of error in a calculation that is based on using a persons stride length of 26 inches plus/minus 2 inches, and the person uses stride length to measure the length and width of a plot of land.
determine the estimated error in calculating the area of the plot of land. step 1 stride - length measurement
the persons stride length is 26 inches with a possible error of ±2 inches. this means the actual stride length can vary between 24 inches and

step 2: calculating the area of the plot
to estimate the error in calculating the area, consider the maximum possible error. assume the person uses their stride length to measure both the

width of the plot.
these are the two measurements we use to calculate area.

step 3: maximum error in length measurement
if the person measures the length using the minimum stride length (24 inches), the actual length could be shorter.
if the person measures the length using the maximum stride length (28 inches), the actual length could be longer.
the difference between these extremes is

step 4: maximum error in width measurement
similar to the length, the maximum error in width measurement is also

step 5: estimated error in area calculation
the area of the plot is calculated as the product of length and width: area = length×width.

• suppose the person uses their stride length to measure the length and width of a rectangular plot.
• lets assume:
• length of the plot = 5 strides.
• width of the plot = 3 strides.
• using the maximum stride length (28 inches)

Explanation:

Step1: Find the maximum stride length

The stride length is 26 inches plus/minus 2 inches. The minimum is 24 inches and the maximum is 26 + 2=28 inches.

Step2: Identify the two - measurement types for area

To calculate the area of a plot, we use length and width measurements.

Step3: Calculate maximum error in length measurement

The difference between the minimum (24 inches) and maximum (28 inches) stride lengths used for length - measurement is 28 - 24 = 4 inches.

Step4: Determine maximum error in width measurement

Since the error in stride length is the same for all measurements, the maximum error in width measurement is also 4 inches.

Step5: Estimate error in area calculation

Let the length be measured as 5 strides and width as 3 strides.
Using maximum stride length of 28 inches, area $A_{max}=28\times5\times28\times3 = 28^2\times15=11760$ square inches.
Using minimum stride length of 24 inches, area $A_{min}=24\times5\times24\times3=24^2\times15 = 8640$ square inches.
The estimated error in area is $11760 - 8640=3120$ square inches.

Answer:

1. 28
2. length
3. 4
4. 4
5. 3120 square inches