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?
A. 34square root of 2 inches
B. 17square root of 3 inches
C. 17square root of 2 inches
D. 13 inches
Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with one side measuring 34 inches (the hypotenuse). Let's call the other two sides x inches.
According to the Pythagorean theorem, we have:
x^2 + x^2 = 34^2
2x^2 = 1156
Dividing both sides by 2, we get:
x^2 = 578
Taking the square root of both sides, we get:
x = square root of 578
Therefore, the side length of each piece is the square root of 578 inches.
Approximately, the square root of 578 is 24.07 inches.
None of the given options match this result.
Since the hypotenuse of the triangle is the longest side and is equal to 34 inches, we can use the Pythagorean theorem to find the lengths of the other two sides:
a^2 + b^2 = c^2
where a and b are the two legs of the right triangle, and c is the hypotenuse. In this case, we have:
a^2 + b^2 = 34^2
a^2 + b^2 = 1156
We also know that the two legs of the triangle are equal (since the square was cut on the diagonal, resulting in two congruent triangles), so we can substitute a = b into the equation above:
2a^2 = 1156
a^2 = 578
a = sqrt(578)
The side length of each piece is equal to a, so the answer is:
A. 34sqrt(2) inches