Final answer:
The length D(x) of the diagonal of a double square of width x is found using the Pythagorean theorem. The formula is D(x) = x√5, derived from the squares of the sides of a right triangle formed by the width x and double width 2x.
Step-by-step explanation:
To determine the length of the diagonal of a double square, you need to consider the dimensions of the resulting shape when two squares of width x are placed side by side. This means that the length of one side of the double square is x, and the length of the other side is 2x, as it consists of two squares' widths combined. Applying the Pythagorean theorem, which states that in a right triangle the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, we can find the diagonal D(x).
The formula according to the Pythagorean theorem would be: D(x) = √x² + (2x)². Simplifying the formula we get D(x) = √x² + 4x², which simplifies further to D(x) = √5x². Therefore, the length of the diagonal is D(x) = x√5.