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There is a point inside an equilateral triangle which is at a distance 1,2 and 3 from three sides . the area of triangle ________

There is a point inside an equilateral triangle which is at a distance 1,2 and 3 from three sides . the area of triangle ________

Grade:11

2 Answers

Vinti Singhai
askIITians Faculty 8 Points
9 years ago
Assume triangle to be ABC and point inside be P.Let each side be''a''.ar(ABC) = ar9PAB) +ar(PBC) + ar(PAC)Root3*a^2/4=1/2*a*1+1/2*a*2+1/2*a*3Get a and then the area.                                                                     Vinti SinghaiaskIITians Faculty,B.E(Honors) in Elec &Comm, Gold Medalist
Aditya kulkarni
21 Points
6 years ago
First consider ๐Ÿ”บ ABC... Triangle ABC is an equilateral triangle.. Let the point inside the triangle be `P`.... According to Viviana`s theorem (search on internet for more details about theorem) sum of distance is equal to the height on equilateral triangle ๐Ÿ”บ which is 1+2+3=6.... Let the altitude meet base at point M.. In triangle AMB, by tan60=AM/BM...BM=2โˆš3.. Total base (BC) is 2*BM..Hence BC=4โˆš3.. Now, Area of triangle ABC = 1/2*BC*AM..Hence,area of triangle ABC ๐Ÿ”บ is 12โˆš3.. .. Thanks for reading... ๐Ÿ˜Š

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