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?

Answer 1

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.