Answer: 19 by 19 meters
Explanation:
The perimeter of a square is given by 4 * side_length. So, the perimeter of the larger square is 4y and the perimeter of the smaller square is 4x. According to the problem, 4y = 4x + 12. We can simplify this to y = x + 3.
The area of a square is given by side_length^2. So, the area of the larger square is y^2 and the area of the smaller square is x^2. According to the problem, y^2 = x^2 + 105.
Now we can substitute y = x + 3 from the first equation into the second equation:
(x + 3)^2 = x^2 + 105
Expanding and simplifying gives us:
x^2 + 6x + 9 = x^2 + 105
Subtracting x^2 from both sides gives:
6x + 9 = 105
Subtracting 9 from both sides gives:
6x = 96
Finally, dividing both sides by 6 gives:
x = 16
Substituting x = 16 into y = x + 3 gives y = 19.
So, the side length of the larger garden is 19 meters.