The area of a square is stored in a double variable named area. write an expression whose value is length of the diagonal of the square.

To find the length of the diagonal of a square when you know the area, you can use the following steps. Given that the area of the square is stored in a double variable named `area`, the formula to find the side length of the square is:

1. Calculate the side length of the square by taking the square root of the area. If `s` is the side length: s = sqrt(area)

2. Then, use the Pythagorean theorem for the diagonal (let's denote it as `d`) of the square, which states: d^2 = s^2 + s^2

Since both sides are equal in a square, this simplifies to:

d^2 = 2 * s^2

To find the diagonal length, you take the square root of both sides:

d = sqrt(2) * s

Substituting `s` from step 1, we get the final expression:

d = sqrt(2) * sqrt(area)

Therefore, the expression to calculate the diagonal's length in terms of the `area` double variable would be: sqrt(2 * area)

In code, assuming you have a function `sqrt` to calculate the square root, the expression would look like this:

double diagonal = sqrt(2 * area);

This calculates the length of the diagonal of the square.

Extra: The concept being used here is the relationship between the area of a square and its sides, as well as the relationship of its sides to the diagonal. A square is a four-sided figure with all sides equal and all angles equal to 90 degrees. The area of a square is calculated by squaring one of its sides (Area = side^2).

When it comes to the diagonal, because the square has right angles, the diagonal forms a right triangle with two of the sides. We can apply the Pythagorean theorem to this right triangle, which states that the square of the hypotenuse (the side opposite the right angle, which in the case of a square is the diagonal) is equal to the sum of the squares of the other two sides. Since the square has all sides equal, this simplifies to twice the square of one side, thus leading to the equation mentioned where d^2 = 2 * s^2. Taking the square root of both sides gives us the length of the diagonal.

Understanding these relationships helps in solving various geometric problems involving squares, and knowing the Pythagorean theorem is fundamental to working with right triangles. The double type in programming is used to store floating-point numbers, which are numbers that can have fractions (decimal points), which is necessary when working with non-integer values such as square roots that may not be whole numbers.