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We can use the Pythagorean theorem to solve this problem. Let the side length of the quilt pieces be x inches.
The hypotenuse of the triangle is 34 inches and the other two sides are x inches. Using the Pythagorean theorem, we have:
x^2 + x^2 = 34^2
2x^2 = 1156
x^2 = 578
x = sqrt(578)
Thus, the side length of each piece is sqrt(578) inches, which is closest to 24.078 inches.
None of the given answer choices match the calculated value.