Quilt squares are cut on the diagonal to
form triangular quilt pieces. The hypotenuse
of the resulting triangles is 28 inches long.
What is the side length of each piece?
A. 14 inches
B. 14√2 inches
C. 14√3 inches D. 28√2 inches
Since each triangular quilt piece is a right triangle, we can use the Pythagorean theorem to find the length of one of its legs.
Let x be the length of one leg of the triangle. Then we have:
x^2 + x^2 = 28^2
Simplifying and solving for x, we get:
2x^2 = 784
x^2 = 392
x = sqrt(392) = 14*sqrt(2)
Therefore, the side length of each triangular quilt piece is 14*sqrt(2) inches, which is option B.
To find the side length of each triangular quilt piece, we need to determine the length of one of the legs of the right triangle.
Given that the hypotenuse of the triangle is 28 inches long, we can use the Pythagorean theorem to find the length of the legs. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's label one of the legs as x inches. Therefore, the other leg would also be x inches since the triangle is an isosceles right triangle.
Using the Pythagorean theorem:
x^2 + x^2 = 28^2
Simplifying the equation:
2x^2 = 784
Dividing both sides by 2:
x^2 = 392
Taking the square root of both sides:
x = √392
Simplifying the square root:
x = √(4 * 98)
x = 2√98
Factoring out the perfect square:
x = 2√(49 * 2)
x = 2 * 7√2
Simplifying the equation:
x = 14√2
Therefore, the side length of each triangular quilt piece is 14√2 inches.
So, the correct answer is option B. 14√2 inches.
To find the side length of each piece, we need to determine the length of the two legs of each triangle. Since the hypotenuse of the triangles is given as 28 inches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs.
Let's call the length of one leg of the triangle x. Then the length of the other leg can also be x (since the triangle is an isosceles right triangle).
Using the Pythagorean theorem:
x^2 + x^2 = 28^2
2x^2 = 784
x^2 = 392
x = √392
x ≈ 19.8 inches
Since the side length of each piece is x, the correct answer is not given among the options. None of the options provided matches the side length derived from the calculations.