The side length of each piece can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the hypotenuse (c) is 34 inches long. Let's call one side of the triangle a and the other side b. The hypotenuse (c) is opposite the right angle.
Therefore, a^2 + b^2 = c^2
a^2 + b^2 = 34^2
a^2 + b^2 = 1156
Since the sides of the quilt square are cut on the diagonal, we have two right triangles that make up the square. So the side length of each piece (a or b) would be:
a = b = √(1156/2) ≈ √578 ≈ 24.04 inches
Therefore, the side length of each triangular quilt piece would be approximately 24.04 inches.