In an equilateral triangle, 3 coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. Area of triangle is : (a) 4+2√3 , (b) 4√3+6 , 12+(7√3)/4 , (d) 3+(7√3)/4.
Answers
Given : In an equilateral triangle, 3 coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle
To find : area of triangle
Solution:
ref attached picture
Side BC of triangle = BD + DE + EC
tan 30 = radius/BD
=> 1/√3 = 1/BD
=> BD = √3
DE = r + r = 1 + 1 = 2
tan 30 = radius/EC
=> 1/√3 = 1/EC
=> EC = √3
Hence BC = √3 + 2 + √3
= 2(1 + √3)
Area of Equilateral triangle = (√3 / 4) Side²
= (√3 / 4) (2(1 + √3))²
= √3 ( 1 + 3 + 2√3)
= 4√3 + 6
Area of triangle is : 4√3+6
option b is correct
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Answer:
4root3+6
Step-by-step explanation:
pls understand clearly
