Question

if perimeter and area of a circle are numerically equal then radius of that circle is.
(a) 2 Units
(b)Units
(c)4 Units
(d)7 units
​

Answer 1

Given :-

PERIMETER OF CIRCLE = AREA OF THE CIRCLE.

To find :- Radius.

we know that,

Perimeter = 2$\pi$r

Area = $\pi$r²

According to the question,

2$\pi$r = $\pi$r²

By transposing $\pi$r to the RHS (Right Hand Side),

2 = $\dfrac{\pi r^{2} }{\pi r}$

$\pi$r gets cancelled in the numerator and the denominator,

2 = r

Therefore, option (a) 2 units is correct.

VERIFICATION :-

Let us substitute r for 2 units and see if the area and perimeter are equal.

2$\pi$r = $\pi$r²

LHS :

=> 2$\pi$r

=> 2 × $\pi$ × 2

=> 4$\pi$ units

RHS :

=> $\pi$r²

=> $\pi$ × 2²

=> 4$\pi$ units

LHS = RHS

Hence verified.

Extras :-

Perimeter of a square = 4 × side

Area of a square = (side)²

Perimeter of a rectangle = 2(length + breadth)

Area of a rectangle = length × breadth

Perimeter of a rhombus = 4 × side

Area of a rhombus = $\dfrac{1}{2}$ × Diagonal 1 × Diagonal 2

Perimeter of a parallelogram = 2(base + height)

Area of a parallelogram = base × height

Perimeter of a triangle = sum of it's sides

Area of a triangle = $\dfrac{1}{2}$ × base × height