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Answer :
we know that
A square plot of land of dimensions 1 mile x 1 mile is 640 acres
5,280 ft is equal to 1 mile
so
5,280 *5,280 =27,878,400 [tex]ft^{2}[/tex]-------> is equal to 640 acres
by proportion
[tex]\frac{27,878,400}{640} \frac{ft^{2}}{acres} = \frac{x}{1} \frac{ft^{2}}{acres} \\\\640*x=27,878,400 \\\\x= \frac{27,878,400}{640}\\\\ x=43,560\ ft^{2}[/tex]
Find the edge of the square plot
[tex]=\sqrt{43,560} \\= 208.71\ ft[/tex]
therefore
the answer is
[tex]208.71\ ft[/tex]
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Final answer:
To find the edge length for a 1 acre homestead, we find the square root of 43,560 square feet (the area of 1 acre), which gives approximately 208.71 feet as the length needed for each edge of the square.
Explanation:
The question asks approximately how many feet on each edge is needed for a square, 1 acre homestead, given that a square plot of land one mile on each edge is 640 acres and there are 5280 ft/mi. First, we recognize that 1 mile = 5280 feet, and know that the conversion for 1 acre is roughly 43560 square feet (since 1 mile squared = 640 acres and 5280 ft * 5280 ft = 27,878,400 sq ft; [tex]27,878,400 sq ft /[/tex] 640 acres = [tex]43,560 sq ft/acre).[/tex]
To find the length of one edge for a 1 acre homestead, we take the square root of 43,560 sq ft (the area of 1 acre) to find the length of each side.[tex]\(\sqrt{43560} \approx 208.71 ft\)[/tex]. Therefore, each edge of a square, 1 acre homestead needs to be approximately 208.71 feet.
