Question

The area of circle inscribed in an equilateral triangle is 154 sq cm. What is the perimeter of the triangle?

(A) 21 cm (B)42√3 cm (C)21√3 cm(D)42 cm

​

Answer 1

Answer:

Let r be the radius of the inscribed circle.

Given that, Area

=

154

c

m

2

⇒

π

r

2

=

154

⇒

r

=

7

c

m

Let a be the side and h height of the triangle. From properties of an equilateral triangle, we know that the point O divides AD in the ratio 2:1.

So,

r

=

h

3

⇒

h

=

3

r

=

21

c

m

Now, altitude,

h

=

√

3

2

a

⇒

a

=

2

h

√

3

=

42

√

3

=

14

√

3

c

m

Hence, perimeter

=

3

a

=

3

×

14

√

3

c

m

=

72.7

c

m