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To find the side length of each piece, we can use the Pythagorean Theorem.
Let x be the side length of each piece. Then, using the Pythagorean Theorem, we have:
x^2 + x^2 = 34^2
2x^2 = 1156
x^2 = 578
x = √578
x ≈ 24.04 inches
Therefore, the side length of each quilt piece is approximately 24.04 inches.