A real estate agent measured a rectangular vacant lot as having a length of 50 yards and a width of 30 yards. Her measurements were accurate to the nearest yard. What is the range of possible values for A, the actual area in: yards of the vacant lot?
To find the range of possible values for A, we need to consider the potential maximum and minimum values of the length and width within the given accuracy.
The maximum potential length would be if the actual length was 50.5 yards (0.5 yards more than the measured length of 50 yards). The maximum potential width would be if the actual width was 30.5 yards (0.5 yards more than the measured width of 30 yards).
Therefore, the maximum potential area would be 50.5 yards * 30.5 yards = 1,527.5 square yards.
The minimum potential length would be if the actual length was 49.5 yards (0.5 yards less than the measured length of 50 yards). The minimum potential width would be if the actual width was 29.5 yards (0.5 yards less than the measured width of 30 yards).
Therefore, the minimum potential area would be 49.5 yards * 29.5 yards = 1,460.25 square yards.
Therefore, the range of possible values for A, the actual area in square yards of the vacant lot, is 1,460.25 to 1,527.5 square yards.
To determine the range of possible values for the actual area of the vacant lot (A), we need to consider the maximum and minimum values that can be obtained based on the given measurements.
1. Maximum possible value for A:
The length and width were measured accurately to the nearest yard. This means that the actual length could be anywhere between 49.5 and 50.5 yards, and the actual width could be anywhere between 29.5 and 30.5 yards. Taking the maximum values, we get:
Actual Length = 50.5 yards
Actual Width = 30.5 yards
Maximum Area (A_max) = Actual Length × Actual Width = 50.5 × 30.5 = 1,542.25 square yards
2. Minimum possible value for A:
Similarly, taking the minimum values, we get:
Actual Length = 49.5 yards
Actual Width = 29.5 yards
Minimum Area (A_min) = Actual Length × Actual Width = 49.5 × 29.5 = 1,459.25 square yards
Therefore, the range of possible values for A, the actual area of the vacant lot, is between 1,459.25 and 1,542.25 square yards.
To find the range of possible values for the actual area of the vacant lot, we need to consider the maximum and minimum possible values based on the given measurements.
The length of the lot is measured as 50 yards, accurate to the nearest yard. This means that the actual length could be as little as 49.5 yards (50 - 0.5) or as much as 50.5 yards (50 + 0.5).
The width of the lot is measured as 30 yards, accurate to the nearest yard. This means that the actual width could be as little as 29.5 yards (30 - 0.5) or as much as 30.5 yards (30 + 0.5).
To find the range of possible values for the area, we calculate the area using these extremities of length and width:
Minimum length = 49.5 yards
Maximum length = 50.5 yards
Minimum width = 29.5 yards
Maximum width = 30.5 yards
Minimum area = Minimum length * Minimum width = 49.5 yards * 29.5 yards
Maximum area = Maximum length * Maximum width = 50.5 yards * 30.5 yards
Now we can calculate the range of possible values for the area:
Minimum area = 1,457.75 square yards
Maximum area = 1,541.75 square yards
Therefore, the range of possible values for the actual area of the vacant lot is between 1,457.75 square yards and 1,541.75 square yards.