Question

The length of a rectangular plot of land is 5 times the width.

If the perimeter is 1000 feet, find the dimensions of the plot.
Round to one decimal place if necessary.

Answer 1

Width ≈ 83.3 feet

Length ≈ 416.7 feet.

Explanation:

We know that the length of the plot is 5 times the width. Let's call the width "
`w`". Then, the length would be "
`5w`".

We also know that the perimeter of the plot is 1000 feet. The formula for the perimeter of a rectangle is:

`\Large \boxed{\textsf{Perimeter = 2 $*$ (Length $*$ Width)}}`

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Calculating

We can substitute the values we have into this formula and solve for "
`w`":

`\bullet 1000 = 2 * (5w + w)\\\bullet 1000 = 2 * 6w\\\bullet 1000 = 12w\\\bullet w = 83.33`

Therefore, the width of the plot is approximately 83.33 feet. We can use this value to find the length:

`\bullet \textsf{Length = 5\textit{w}}\\\bullet \textsf{Length = 5 $*$ 83.33}\\\bullet \textsf{Length = 416.67}`

Therefore, the length of the plot is approximately 416.67 feet.

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Rounding

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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