AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

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

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

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.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!