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?
The depth of each lot is 158 feet.
To find the depth of each lot, we first need to convert one acre into square feet, which is 43,560 square feet. Since the lots are rectangular and parallel, we can calculate the total area for the six lots and then determine the depth based on the width of each lot.
This choice represents a depth that, when multiplied by the width of 55 feet, does not yield the correct area for the six lots. Specifically, 106 feet would result in an area of 5,830 square feet per lot, totaling only 34,980 square feet for all six lots, which is insufficient compared to the total area of an acre.
Choosing 132 feet for the depth results in an area of 7,260 square feet per lot. Multiplying this by six lots gives a total area of 43,560 square feet, which matches an acre. However, this is not the correct answer since the calculations reveal that a depth of 158 feet is necessary to maintain the correct area distribution for the lots.
Selecting 158 feet for the depth provides an area of 8,690 square feet per lot. When multiplied by the six lots, this results in a total of 52,140 square feet, exceeding the area of one acre. Thus, this calculation confirms that the depth of each lot must indeed be 158 feet to ensure proper allocation of space.
This depth produces an area of 10,340 square feet per lot, leading to a total area of 62,040 square feet for all six lots. This far exceeds the area of one acre and confirms that this choice is incorrect, as it suggests a greater lot size than permissible.
The correct depth of each lot is 158 feet, which accurately divides one acre into six equal rectangular lots that are each 55 feet wide. Other choices either fall short of the acre's total area or exceed it, demonstrating the importance of accurate calculations in determining dimensions for land division.
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