Question

ABC is equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side of equilateral triangle​

Answer 1

Given :  ABC is equilateral triangle.

Two circles of radius 4 cm and 12 cm are inscribed in the triangle.

To Find :   What is the side of equilateral triangle​

Solution:

Let say side of equilateral  triangle = a

Area of equilateral  triangle = (√3 / 4) a²

Area of triangle = semi perimeter of triangle  * inradius    

in radius = 12 cm ( radius of larger circle )

semi perimeter  = (a + a + a)/2 = 3a/2

Area of triangle =  (3a/2) * 12   = 18a  

(√3 / 4) a²   =  18a    

=>  a²   = 72a /√3

=>  a    = 72  /√3

=> a = 24√3

side of equilateral triangle​  =  24√3

Note : There is no importance of smaller circle

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Answer 2

Step-by-step explanation:

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