Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 34 inches long. What is the side length of each piece?
To find the side length of each triangular quilt pieces, we can use the Pythagorean theorem, which states that the square of the hypotenuse (34 inches) is equal to the sum of the squares of the other two sides.
Let's say the side lengths of the two smaller sides are x and y inches. Then we have:
x^2 + y^2 = 34^2
Since the triangles are formed by cutting quilt squares on the diagonal, we know that x = y. So we can rewrite the equation as:
2x^2 = 34^2
x^2 = 34^2 / 2
x^2 = 1156
x = sqrt(1156)
x = 34 inches
Therefore, the side length of each triangular quilt piece is 34 inches.