Unknown X in rectangle

I'm assuming that what you drew is a parabola. Is that a reasonable assumption?

If so, the equation of your parabola is y = cx², assuming that the vertex is at (0, 0). From the drawing, the points (b, 3) and (-b, 3) are on the parabola.

The arc length shown in the drawing is the length along the curve between (-b, 3) and (b, 3). Due to symmetry, we can work with half this length, or 3 units.

Since y = cx², then y' = 2cx, which I will use in the formula for arc length. Also, since (b, 3) is a point on the curve, then 3 = c*b².

This equation equates the arc length integral with the known length:
$$ \int_0^b \sqrt{1 + (2cx)^2}dx = 3$$

This gives you two equations in the unknowns b and c, so it should be possible to determine b and c.