The area of the lot, based on the range of the variable 'y' being from 8 to 10 yards, can only be 64, 81, or 100 square yards. None of the provided options (183, 323, 171, 193 square yards) match the calculated areas of the lot.
The area of the lot is represented by the formula A = y × y, which can be also written as A = y^2. Since the developer has determined that y is within the range of 8 yards to 10 yards, inclusive, we can calculate the minimum and maximum areas possible for the lot by squaring these values of y.
For y = 8 yards, the area is 8 × 8 = 64 yd^2.
For y = 9 yards, the area is 9 × 9 = 81 yd^2.
For y = 10 yards, the area is 10 × 10 = 100 yd^2.
Thus, the correct answer for the area of the lot, considering the given options, is none of the available choices, since all of them are outside the calculated range of areas.
The probable question may be:
A developer purchases an empty lot with dimensions represented by the variable "y" in yards (yd) to construct a small house. The area of the lot is given by the formula A=y×y square yards. Considering the potential values for "y," which of the following options accurately represents the area of the lot?
Options:
A. 183 yd^2
B. 323 yd^2
C. 171 yd^2
D. 193 yd^2
Additional Information:
Let's consider that the developer has surveyed the lot and found that the value of "y" lies within the range of 8 yards to 10 yards, inclusive. The area of the lot is directly proportional to the square of the side length. Therefore, by squaring each value within the specified range, we can determine the corresponding areas and choose the correct option.
y (yd) Area (A=y×yA=y×y, yd²)
8 64
9 81
10 100
Based on this information, you can determine the correct answer among the given options.