Question

PLEASE HELP!!!!!!! ALSO SHOW WORK

You 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?

Answer 1

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. yd

Let the length of each side be 'a'.

As we know the formula for "Area":

$Area=a^2\\\\529=a^2\\\\\sqrt{529}=a\\\\a=23\ yd$

So, the perimeter of the square pen is given by

$4\times s=4\times 23\\\\=92\ yd$

So, perimeter of square pen = Perimeter of round pen

$92=2\pi r\\\\92=2\times 3.14\times r\\\\\dfrac{92}{2}=3.14\times r\\\\\dfrac{46}{3.14}=r\\\\14.64=r$

So, the diameter of round pen is $2\times r=2\times 14.64=29.29\ yd$

And the area of round pen is

$\pi r^2\\\\=3.14\times (14.64)^2\\\\=672.99\ sq.\ yd$

Hence, a) 92 yards, b) 29.29 yards and 672.99 sq. yd.