Wednesday, December 24, 2008

Elearn Geometry Problem 212: 120 Degree Triangle, Areas

Problem 211: Equilateral Triangle, Area

See complete Problem 212 at:
gogeometry.com/problem/p212_triangle_120_equilateral_area.htm

120 degrees triangle, equilateral triangle, areas. Level: High School, SAT Prep, College geometry

1 comment:

  1. Sa= (root3)*a^2/4
    Sb= (root3)*b^2/4
    Sc= (root3)*c^2/4
    S= 1/2*ac*Sin 120=(root3)*ac/4
    but by cosine rule
    b^2=a^2+c^2+ac so ac= b^2- a^2- c^2
    s=(root3)/4*ac
    = (root3)/4[b^2-c^2-a^2]
    = Sb-Sc-Sa
    hence Sb=Sa+Sc+S -----(1)
    but S^2=Sa*Sc
    S= root of (Sa*Sc)
    substitute in equation 1
    we get Sb=Sa+Sc+ root of (Sc*Sa)
    hence solved.

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