For this case we have that by definition, the area of a square is given by:[tex]A = l ^ 2[/tex]
Where:
l: It's the side of the square
We have as data that:
[tex]A = 64x ^ 2 * y ^ 4[/tex]
So:
[tex]64x ^ 2 * y ^ 4 = l ^ 2[/tex]
We cleared l, applying root to both sides:
[tex]l = \pm \sqrt {64x ^ 2 * y ^ 4}[/tex]
We choose the positive value of the root:
[tex]l = \sqrt {64x ^ 2 * y ^ 4}\\l = 8xy ^ 2[/tex]
So, the side of the square is: [tex]8xy ^ 2[/tex]
The perimeter is given by:
[tex]P = 4l\\P = 4 (8xy ^ 2)\\P = 32xy ^ 2[/tex]
Answer:
[tex]l = 8xy ^ 2\\P = 32xy ^ 2[/tex]
