Understanding the Area of a Rhombus
The area \( A \) of a rhombus can be expressed using the formula:
\[ A = \frac{1}{2} \times d_1 \times d_2 \]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals. Given that the area of the rhombus is \( x^2 \), we can set up the equation:
\[ \frac{1}{2} \times d_1 \times d_2 = x^2 \]

Expressing the Diagonals
We can express the diagonals in terms of one diagonal. Assume \( d_1 \) is the longer diagonal and \( d_2 \) is the shorter diagonal. Then, we can denote \( d_2 \) as \( d \). Thus, we can rewrite the area equation:
\[ \frac{1}{2} \times d_1 \times d = x^2 \]
From this point, we can isolate \( d_1 \):
\[ d_1 = \frac{2x^2}{d} \]

Finding the Relationship Between Diagonals
In a rhombus, the diagonals bisect each other at right angles. We can use the Pythagorean theorem to relate the sides of the rhombus with the diagonals:
\[ a^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 \]
where \( a \) is the length of a side of the rhombus. However, we need to focus on the relationships we derived earlier.

Conclusion: The Longer Diagonal
From the area formula and rearranging it, the longer diagonal \( d_1 \) can be expressed as follows:
\[ d_1 = \frac{2x^2}{d} \]
This relationship allows you to determine the longer diagonal provided you have the length of the shorter diagonal \( d \). Thus, knowing one diagonal enables you to compute the other and fully understand the dimensions of the rhombus.