Maths-
General
Easy

Question

# In any equilateral Δ, three circles of radii one are touching to the sides given as in the figure then area of the Δ

Hint:

### Here, we have to find the area of the equilateral triangle.Firstly, we have given equilateral triangle, ABC, in fig, Here three circle inside the triangle, and their radii is 1 and center PQR, so we can write,QD = 1, RE = 1, PF = 1. ∠ACB = 60° ( angle of equilateral triangle)∠QCD = 30° ( intersection of angle ACB)So ,tan 30° = = [ since tan 30° = and QD = 1] CD = Similarly, EB = DE = QR = 1 +1= 2 So, CB = CD + DE + EB CB = ++ CB = 2 + = 2(1+ )unitCB is side of triangle,Since, the area of triangle, Area = x side2 = x (2(1+))2 = x 4 ( 1 + )2 = x ( 1 + 3 + ) = + + 2 x 3 = + 6 unitTherefore, the correct answer is 6+

In this question, we have to find the area of the triangle, The formula of area of equilateral triangle is  x side2. Find the length of one side of the triangle in which  you have three circle is given with radius 1 unit.