Find the diameter of the circle that has a circumference equal to its area.
2
4
8
10

The formula for circumference of a circle:


The formula for area of a circle:

r - radius

The circumference is equal to the area.


The diameter is two times the radius.

Circumference may have the same numerical magnitude as area, but they will never be "equal".  Circumference is a length or distance, and area is an area.
So they can never have the same units, and quantities can't be equal without
the same units.

You might say that   π D (circumference) = π (D/2)²  (area) .

Then  D = (D/2)²

           D = D² / 4

           1 = D / 4

           D = 4 .

But this is no more than a parlor trick.  In order to do it, you need to
ignore units completely, and that's unacceptable in math.