This problem relies on the knowledge of the equation for the area of a rhombus, , where  is the area, and  and  are the lengths of the individual diagonals. We can substitute the values that we know into the equation to obtain:

Therefore, our final answer is that the diagonal 

The area of a rhombus is given below.

Substitute the given area and a diagonal.  Solve for the other diagonal.

The area of a rhombus is given below. Plug in the area and the given diagonal. Solve for the other diagonal.

Let the shorter diagonal be , and the longer diagonal be .  The longer dimension is twice as long as the other diagonal.  Write an expression for this.

Write the area of the rhombus.

Since we are solving for the shorter diagonal, it's best to setup the equation in terms , so that we can solve for the shorter diagonal.  Plug in the area and expression to solve for .

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  to find the length of diagonal . From the problem, we are given that the sides are  and . Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  to find the length of diagonal . From the problem, we are given that the sides are  and . Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  to find the length of diagonal . From the problem, we are given that the sides are  and . Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  and use the Pythagorean Theorem to solve for . From the problem:

Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,

Using the quadratic formula,

With this equation, we get two solutions:

Only the positive solution is valid for this problem.

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  and use the Pythagorean Theorem to solve for . From the problem:

Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,

Factoring,

 and 

The first solution is nonsensical for this problem. 

A rhombus is a quadrilateral with four sides of equal length. Rhombuses have diagonals that bisect each other at right angles.

Thus, we can consider the right triangle  to find the length of side . From the problem, we are given  and . Because the diagonals bisect each other, we know:

Using the Pythagorean Theorem,