Answer:
Width ≈ 83.3 feet
Length ≈ 416.7 feet.
Step-by-step explanation:
We know that the length of the plot is 5 times the width. Let's call the width "[tex]w[/tex]". Then, the length would be "[tex]5w[/tex]".
We also know that the perimeter of the plot is 1000 feet. The formula for the perimeter of a rectangle is:
[tex]\Large \boxed{\textsf{Perimeter = 2 $\times$ (Length $\times$ Width)}}[/tex]
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We can substitute the values we have into this formula and solve for "[tex]w[/tex]":
[tex]\bullet 1000 = 2 \times (5w + w)\\\bullet 1000 = 2 \times 6w\\\bullet 1000 = 12w\\\bullet w = 83.33[/tex]
Therefore, the width of the plot is approximately 83.33 feet. We can use this value to find the length:
[tex]\bullet \textsf{Length = 5\textit{w}}\\\bullet \textsf{Length = 5 $\times$ 83.33}\\\bullet \textsf{Length = 416.67}[/tex]
Therefore, the length of the plot is approximately 416.67 feet.
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Since the problem asks us to round to 1 decimal place if necessary, we can round the width to 83.3 feet and the length to 416.7 feet.
Therefore, the dimensions of the rectangular plot of land are approximately 83.3 feet by 416.7 feet.
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