Question

determine the estimated error in calculating the area of the plot of land. step 1 stride length measurement the persons stride length is 25 inches with a possible error of ±2 inches. this means the actual stride length can vary between 23 inches and __ inches. 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 and 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 (23 inches), the actual length could be shorter. if the person measures the length using the maximum stride length (27 inches), the actual length could be longer. the difference between these extremes is inches. step 4: maximum error in width measurement similar to the length, the maximum error in width measurement is also inches. 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 (27 inches): length = 5 strides × 27 inches = 135 inches width = 3 strides × 27 inches = 81 inches maximum area = length × width = 135 inches × 81 inches = square inches. using the minimum stride length (23 inches): length = 5 strides × 23 inches = 115 inches width = 3 strides × 23 inches = 69 inches minimum area = length × width = 115 inches × 69 inches = 7935 square inches. the actual area lies between the maximum and minimum calculated areas. error = maximum area - minimum area error = 10935 square inches - 7935 square inches = __ square inches.

Explanation:

Step1: Find the maximum stride length

The person's stride length is 25 inches with a possible error of ±2 inches. So the maximum stride length is $25 + 2=27$ inches.

Step2: Identify the dimensions for area calculation

To calculate the area of a rectangle, we use length and width. So the person uses their stride - length to measure both the length and width of the plot.

Step3: Calculate the difference in length measurement extremes

The minimum stride length is 23 inches and the maximum is 27 inches. The difference is $27-23 = 4$ inches.

Step4: Determine the maximum error in width measurement

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

Step5: Calculate the maximum area

Using the maximum stride length (27 inches), if length = 5 strides and width = 3 strides, then length $l=5\times27 = 135$ inches and width $w = 3\times27=81$ inches. The maximum area $A_{max}=l\times w=135\times81 = 10935$ square inches.

Step6: Calculate the minimum area

Using the minimum stride length (23 inches), length $l = 5\times23=115$ inches and width $w=3\times23 = 69$ inches. The minimum area $A_{min}=l\times w=115\times69 = 7935$ square inches.

Step7: Calculate the estimated error in area

The error $E=A_{max}-A_{min}=10935 - 7935=3000$ square inches.

Answer:

27; length; 4; 4; 10935; 3000