Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units
(B) `pi`units
(C) 4 units
(D) 7 units

Explanation

To solve the problem, we need to find the radius of a circle where the perimeter (circumference) and the area are numerically equal. Let's go through the steps:

### Step 1: Understand the formulas
The formulas we need are:
- The circumference (perimeter) of a circle: \( C = 2\pi r \)
- The area of a circle: \( A = \pi r^2 \)

### Step 2: Set up the equation
According to the problem, the circumference is equal to the area:
\[ 2\pi r = \pi r^2 \]

### Step 3: Simplify the equation
We can simplify this equation by dividing both sides by \( \pi \) (assuming \( \pi \neq 0 \)):
\[ 2r = r^2 \]

### Step 4: Rearrange the equation
Rearranging gives us:
\[ r^2 - 2r = 0 \]

### Step 5: Factor the equation
We can factor this equation:
\[ r(r - 2) = 0 \]

### Step 6: Solve for \( r \)
Setting each factor to zero gives us:
1. \( r = 0 \) (not a valid solution for a radius)
2. \( r - 2 = 0 \) which gives \( r = 2 \)

### Conclusion
The radius of the circle is \( r = 2 \) units. Therefore, the correct answer is (A) 2 units.

---