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JEE Main201911 Jan 2019Evening ShiftMathematicsProperties of TrianglesActual

Given b + c 11 = c + a 12 = a + b 13 for a ABC with usual notation. If A = B = C , then the ordered triad ( , , ) has a value

Options

  1. A(7,19,25)
  2. B(3,4,5)
  3. C(5,12,13)
  4. D(19,7,25)

Correct answer

A. (7,19,25)

Step-by-step solution

Let b+c 11 = c+a 12 = a+b 13 =k (Say). b+c=11 k, c+a=12 k, a+b=13 k a+b+c=18 k a=7 k, b=6 k and c=5 k A= 36 k²+25 k²-49 k² 2.30 k² = 1 5 and B= 49 k²+25 k²-36 k² 2.35 k² = 19 35 and C= 49 k²+36 k²-25 k² 2.42 k² = 5 7 A: B: C=7: 19: 25 A 7 = B 19 = C 25 Hence, required ordered triplet is (7,19,25)

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