Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 16 inches long. What is the side length of each piece?
8 in
8√3 in
16√2 in
8√2 in (As of now I think this one is correct)
you are correct
To find the side length of each quilt piece, we need to determine the length of one of the legs of the right-angled triangle formed by cutting the quilt squares on the diagonal.
By using the Pythagorean theorem, we can determine the length of the leg. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of the leg as "x". According to the given information, the hypotenuse of the triangle is 16 inches.
Using the Pythagorean theorem, we have:
x^2 + x^2 = 16^2
Simplifying the equation:
2x^2 = 256
Dividing both sides of the equation by 2:
x^2 = 128
Taking the square root of both sides, we get:
x = √128
Simplifying the square root, we have:
x = √(64 * 2)
Since the square root of 64 is 8:
x = 8√2
Therefore, the side length of each quilt piece is 8√2 inches. The correct answer is 8√2 in.