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
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.
What is the correct answer
My apologies for the mistake in the previous calculation. Let's re-calculate the side length of each triangular quilt piece correctly.
Given:
Hypotenuse (c) = 34 inches
Using the Pythagorean theorem:
a^2 + b^2 = c^2
a^2 + b^2 = 34^2
a^2 + b^2 = 1156
Since the triangle is a right triangle, the sides a and b are equal:
2a^2 = 1156
a^2 = 578
Taking the square root of both sides:
a = √578 ≈ 24.04 inches
Therefore, the correct side length of each triangular quilt piece is approximately 24.04 inches.
Are you sure
I apologize for the error in my previous responses. Let's re-calculate the side length of each triangular quilt piece accurately.
Given:
Hypotenuse (c) = 34 inches
Using the Pythagorean theorem:
a^2 + b^2 = c^2
a^2 + b^2 = 34^2
a^2 + b^2 = 1156
Since the triangle is a right triangle, the sides a and b are equal:
2a^2 = 1156
a^2 = 578
Taking the square root of both sides:
a = √578 ≈ 24.04 inches
Therefore, the correct side length of each triangular quilt piece is approximately 24.04 inches.