Answer:
In a rectangle where the length is twice as long as the width, we can use the Pythagorean theorem to relate the length, width, and diagonal of the rectangle.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In this case, the length of the napkin (l) is one of the sides, and the width of the napkin (w) is the other side. The diagonal (x) is the hypotenuse.
We can set up the equation as follows:
l^2 + w^2 = x^2
Given that the length is twice the width (l = 2w), we can substitute 2w for l in the equation:
(2w)^2 + w^2 = x^2
4w^2 + w^2 = x^2
Combining like terms:
5w^2 = x^2
Taking the square root of both sides:
√(5w^2) = √(x^2)
√5w = x
Therefore, the length of the napkin along the diagonal (x) is √5 times the width (w), or in terms of the given length (l), it is √5 times half the length (l/2).