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Mr. Williams has a circular garden with a diameter of 107 feet, surrounded by fencing.
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Using the same length of fencing, he’s going to create a square garden.
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What is the maximum side length of the square?
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Round the result to one decimal place.
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Here’s Mr. Williams’s circular garden with a diameter of 107 feet.
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We know that this garden is surrounded by fencing. we can find the amount of fencing required by finding the circumference of the circular garden.
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Since we know the diameter, we can find the circumference by multiplying the diameter by 𝜋.
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The circumference of this garden is 107 times 𝜋 rounded to the hundredths place; 107 times 𝜋 equals 336.15.
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It’s measured in feet.
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But what does this value tell us?
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This amount is the amount of fencing used on a circular garden.
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Mr. Williams wants to use this same amount of fencing on a square garden.
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The fencing on a square garden is the perimeter of the square garden, the side length added together four times.
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The perimeter of the square is four times the side length.
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If we want the perimeter of the square, the amount of fencing, to be equal to 336.15, that means that value must be equal to four times the side length.
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To solve for one side, we divide both sides of our equation by four: 336.15 divided by four.
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When we divide both sides by four, we get 84.0375, rounded to one decimal place is 84.0, 84 and zero tenths feet.
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The maximum side length of his square garden would have to be 84.
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This would make the circumference of his circle garden and the perimeter of his square garden almost exactly equal.