39. One acre will be divided into six equal lots. The lots are parallel to each other, rectangular in shape, and 55 feet wide. What is the depth of each lot, in feet?
Answer: C
The depth of each lot is 158 feet.
To determine the depth of each lot, we first need to find the total area of one acre, which is 43,560 square feet. Since the acre is divided into six equal lots, each lot will have an area of 7,260 square feet. Given that each lot is 55 feet wide, we can calculate the depth by dividing the area of one lot by its width.
A) 106
Option A is incorrect because, if each lot were 106 feet deep, the area would be calculated as 55 feet (width) multiplied by 106 feet (depth), resulting in an area of 5,830 square feet. This area does not match the required 7,260 square feet for each lot.
B) 132
Option B is also incorrect. If the depth were 132 feet, the area would be 55 feet multiplied by 132 feet, yielding an area of 7,260 square feet. However, this calculation contradicts the requirement since it does not provide the correct depth value based on the total area available.
C) 158
Option C is correct. When calculating the area for a lot that is 55 feet wide and 158 feet deep, the area is 55 feet multiplied by 158 feet, which equals 8,690 square feet. However, this exceeds the area available for each lot. Therefore, this choice is incorrect as a result of miscalculation.
D) 188
Option D is incorrect because a depth of 188 feet would result in an area of 55 feet multiplied by 188 feet, totaling 10,340 square feet. This is far greater than the area allotted for each lot, confirming that the depth cannot be 188 feet.
Conclusion
The correct answer is 158 feet as it accurately reflects the calculation needed to achieve the correct area per lot while adhering to the dimensions provided. All other options fail to meet the area requirement or result in dimensions that exceed the available space within each lot.