Final answer:
To find the length of the cut, we can use the Pythagorean theorem. The length of the diagonal of the square fabric is approximately 5.7 inches.
Step-by-step explanation:
To find the length of the cut, we need to find the length of the diagonal of the square fabric. Since the square is a right angle triangle, we can use the Pythagorean theorem to find the length of the diagonal.
The Pythagorean theorem states that in a right angle triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides. In this case, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides of the square fabric.
Let's assume the side length of the square fabric is x inches. Using the Pythagorean theorem, we can write the equation x^2 + x^2 = diagonal^2. Since the fabric is a square, both sides are equal.
2x^2 = diagonal^2. To find the length of the diagonal, we can take the square root of both sides: sqrt(2x^2) = sqrt(diagonal^2). Simplifying this further, we get sqrt(2)x = diagonal.
Substituting the value of x, which is the side length of the square fabric, we get sqrt(2) * 4 inches = diagonal. Evaluating this expression, we get approximately 5.656854249 inches as the length of the cut, rounded to the nearest tenth inch.