Video: Finding the Side Length of a Square with the Same Perimeter as a Given Circle

Mr. William has a circular garden with a diameter of 107 feet surrounded by fencing. Using the same length of fencing, he is going to create a square garden. What is the maximum side length of the square? Round the result to one decimal place.

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Video Transcript

Mr. Williams has a circular garden with a diameter of 107 feet, surrounded by fencing. Using the same length of fencing, he’s going to create a square garden. What is the maximum side length of the square? Round the result to one decimal place.

Here’s Mr. Williams’s circular garden with a diameter of 107 feet. 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. Since we know the diameter, we can find the circumference by multiplying the diameter by 𝜋.

The circumference of this garden is 107 times 𝜋 rounded to the hundredths place; 107 times 𝜋 equals 336.15. It’s measured in feet. But what does this value tell us? This amount is the amount of fencing used on a circular garden. Mr. Williams wants to use this same amount of fencing on a square garden.

The fencing on a square garden is the perimeter of the square garden, the side length added together four times. The perimeter of the square is four times the side length. 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.

To solve for one side, we divide both sides of our equation by four: 336.15 divided by four. When we divide both sides by four, we get 84.0375, rounded to one decimal place is 84.0, 84 and zero tenths feet. The maximum side length of his square garden would have to be 84. This would make the circumference of his circle garden and the perimeter of his square garden almost exactly equal.

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