PLEASE HELP!!!!!!! ALSO SHOW WORKYou have enough fencing to create square pen with an area of 529 yd.2 Find the length of each side of the fence. What would be the perimeter of the square pen? If you wanted to take the fencing and create a round pen, what would be the diameter and the area of the round pen (Use π = 3.14 and round to the nearest hundredth). Does the square pen or round pen give you the greatest area?
Accepted Solution
A:
Answer: a) 92 yards, b) 29.29 yards and 672.99 sq. yd.Step-by-step explanation:Since we have given that Area of square pen = 529 sq. ydLet the length of each side be 'a'.As we know the formula for "Area":[tex]Area=a^2\\\\529=a^2\\\\\sqrt{529}=a\\\\a=23\ yd[/tex]So, the perimeter of the square pen is given by[tex]4\times s=4\times 23\\\\=92\ yd[/tex]So, perimeter of square pen = Perimeter of round pen [tex]92=2\pi r\\\\92=2\times 3.14\times r\\\\\dfrac{92}{2}=3.14\times r\\\\\dfrac{46}{3.14}=r\\\\14.64=r[/tex]So, the diameter of round pen is [tex]2\times r=2\times 14.64=29.29\ yd[/tex]And the area of round pen is [tex]\pi r^2\\\\=3.14\times (14.64)^2\\\\=672.99\ sq.\ yd[/tex]Hence, a) 92 yards, b) 29.29 yards and 672.99 sq. yd.