Answer: 61.52 cm and 38.48 cm
Explanation:
A 100 cm wire is going to be cut into two pieces (A and B) and transformed into squares. To facilitate calculations, we can say that
A = 4x and B = 4y
as A + B = 100
4x + 4y = 100
Piece A, with a perimeter of 4x, is a square of x as a side and x² as area.
Piece B, with a perimeter of 4y, is a square of y as a side and y² as area.
We know that x² + 144 = y² → x² - y² = 144
4x + 4y = 100 → x + y = 25 (1)
x² - y² = 144 → (x-y)(x+y)=144 (2)
Substituting (1) in (2)
(x-y) . 25 = 144
(x-y) = 144/ 25
x - y = 5.76
Resolving the system:
x + y = 25
x - y = 5.76
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2x = 30.76
x = 15.38
So A = 4x = 4 . 15.38 = 61.52
B = 100 - 61.52 = 38.48