The length of each side of the fence is 23 yards
The perimeter of the square pen is 92 yards
The diameter of the round pen would be 29.30 yards
The area of the round pen would be 673.91 yards²
The round pen gives the greatest area
Step-by-step explanation:
Let us revise some rules
1. Area of the square = L², where L is the length of its side
2. Perimeter of the square = 4 L
3. Area of the circle = π r², where r is the length of its radius
4. Circumference of the circle = 2 π r
∵ You have enough fencing to create square pen with an area of
529 yd²
∵ Area of the square = L²
∴ L² = 529
- Take √ for both sides
∴ L = 23 yards
The length of each side of the fence is 23 yards
∵ Perimeter of the square = 4 L
∵ L = 23
∴ The perimeter of the square = 4(23) = 92 yards
The perimeter of the square pen is 92 yards
You want to create a round pen using the same fencing
The perimeter of the square pen is equal to the circumference of
the round pen
∵ The perimeter of the square pen = 92 yards
∵ Circumference of the circle = 2 π r
∵ π = 3.14
∴ 92 = 2(3.14) r
∴ 92 = 6.28 r
- Divide both sides by 6.28
∴ r = 14.64968 ≅ 14.65 yards
∵ Diameter of the circle = 2 r
∴ The diameter = 2(14.65)
∴ The diameter = 29.30 yards to the nearest hundredth
The diameter of the round pen would be 29.30 yards
∵ Area of the circle = π r²
∵ r = 14.65 yards
∴ Area of the round pin = 3.14(14.65)²
∴ Area of the round pin = 673.91 yards²
The area of the round pen would be 673.91 yards²
∵ The area of the square pen is 529 yards²
∵ The area of the round pen is 673.91 yards²
∴ The area of the round pen > the area of the square pen
The round pen gives the greatest area
Learn more:
You can learn more about the circle in brainly.com/question/3055705
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