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The area of a circle inscribed in an equilateral triangle is $154 cm 2$ .

Then, the perimeter of the triangle will be ____ $cm$ . $[Take 3 =1 . 73]$

see full answer

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Detailed Solution

The area of a circle inscribed in an equilateral triangle is

154 cm 2

. Then, the perimeter of the triangle will be 72.66 cm.
Given, area of circle is

154 c m 2

.
The area of a circle with radius

r

is given as-

A r e a = π r 2

⇒ π r 2 = 154 ⇒ r 2 = 154 × 722 ⇒ r 2 = 7 × 7 ⇒ r = 7 × 7 ⇒ r = 7 c m

Now, side of an equilateral triangle is-
The radius

r

of a circle inscribed in an equilateral triangle is given as-

r = a 23

where,

a

is the side of an equilateral triangle.

⇒ r = a 23 ⇒ 7 = a 23 ⇒ a = 143 c m

Now, the perimeter of the triangle is-

P e r i m e t e r = 3 a = 3 × 143 = 423 c m

Substituting

3 =1 . 73

, we get,

P e r i m e t e r = 42 × 1.73 = 72.66 c m

Hence,

72.66 c m

is the required perimeter.

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