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AP EAMCET2014MathematicsProperties of Triangles

If in the angles of a triangle are in the ratio 1: 1: 4 , then the ratio of the perimeter of the triangle to its largest side is

Options

  1. A2 +2: 3
  2. B3: 2
  3. C3 +2: 2
  4. D3 +2: 3

Correct answer

D. 3 +2: 3

Step-by-step solution

Given, the ratio of angles of a triangle is 1: 1: 4 . Let angles of a triangle are A, B and C . A: B: C=1: 1: 4 Let A=x, B=x and C=4 x array lc & A+B+C=180^ & x+x+4 x=180^ & 6 x=180^ x=30^ & A=30^ , B=30^ and C=120^ array Hence, largest angle is 120^ . So largest side of a triangle is c . Perimeler ul triangle : Largesl side of a triangle aligned & =(a+b+c): c & = (2 R 30^ +2 R 30^ +2 R 120^ ) aligned 2 R 120^ aligned [ a & =2 R A, b=2 R B and C=2 R C] & =2 R [ 1 2 + 1 2 + 3 2 ]: 2 R 3 2 & = (1+ 3 2 ): 3 2 =2+ 3 :

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