How to find the area of the square $|ABCD|$?

Question

As seen, the graph of this parabola $y = 24 - x^2$ is given. So, I want to find the area of the square $|ABCD|$. However, I've no clue about how to.

Answer 1

From the condition $$OC=2CB \implies y = 24 - x^2=2x \implies x^2+2x-24=0 \implies x=4$$

Answer 2

Hint:

The point $B$ has coordinates $(x, 2x)$.

Answer 3

Hint: As $DC=BC$, the coordinates of $B$ are of the form $(2y,y)$.

Answer 4

Let $C=(x_0,0)$ then $CD=2x_0$ then $BC=24-x_0^2$ also $CD=BC$ so $24-x_0^2=2x_0$ which leads to $x_0=4$ or $x_0=-6$ which is wrong. So $CD=2x_0=8$ and $S_{ABCD}=64$