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MHT CET202410 May 2024Morning ShiftMathematicsProperties of TrianglesActual

If the angles A , B and C of a triangle ABC are in the ratio 2: 3: 7 respectively, then the sides a, b and c are respectively in the ratio

Options

  1. A2: 2 :( 3 +1)
  2. B2 : 2:( 3 +1)
  3. C( 3 +1): 2 : 2
  4. D2:( 3 +1): 2

Correct answer

B. 2 : 2:( 3 +1)

Step-by-step solution

Angles of triangle ABC are in ratio 2: 3: 7 Let the common multiple be x array ll & A=2 x, B=3 x, C=7 x & 2 x+3 x+7 x=180^ array ...[Sum of measure of angles of triangle is 180^ ] array ll & 12 x=180 & x=15 & ~A =30^ , B =45^ ; C =105^ array Now, By sine Rule aligned & a A = b B = c C & a 30^ = b 45^ = c 105^ & a 1 2 = b 1 2 = c 3 +1 2 2 & a 2 = b 2 = c 3 +1 & a: b: c= 2 : 2: 3 +1 aligned

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