In the given figure, ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 24√3
Let the side of the triangle be x.
AD = √3x/2
In △ABE:
sin30º = 4/AB
⇒ AB = 8 cm
AD = 8 + 4 + 24 = 36 cm
⇒ √3x/2 = 36
⇒ x = 72/√3 = 24√3 cm