If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

Let’s denote the radius of the circle as “r.” The perimeter (circumference) of a circle is given by the formula 2πr^2, and the area of the circle is given by the formula πr2.

The problem states that the perimeter and the area are numerically equal, so we can set up the equation:

2πr=πr^2

To solve for the radius r, let’s simplify the equation step by step:

**Divide both sides by π:**

2πr/π=πr^2/π This simplifies to: 2r=r^2

**Rearrange the equation:**

Move all terms to one side to set the equation to zero: r^2−2r=0

**Factor the equation:**

Factor out the common term “r”: r(r−2)=0

This equation holds true if either r=0 or 0r−2=0.

**Solve for r:**- If r=0, it implies a circle with no radius, which is not physically meaningful in this context.
- If r−2=0, then r=2.

Conclusion:

Therefore, the radius of the circle is r=2 units.