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AP EAMCET202315 May 2023Morning ShiftMathematicsProperties of TrianglesActual

In A B C , if A 2 : B 2 : C 2 =3: 7: 9 , then a: b: c=

Options

  1. A8: 6: 5
  2. B5: 6: 8
  3. C10: 8: 5
  4. D5: 8: 10

Correct answer

A. 8: 6: 5

Step-by-step solution

aligned & A 2 : B 2 : C 2 =3: 7: 9 & s(s-a) (s-b)(s-c) : s(s-b) (s-a)(s-c) : s(s-c) (s-a)(s-b) & =3: 7: 9 & s(s-a) (s-b)(s-c) : s(s-b) (s-a)(s-c) : s(s-c) (s-a)(s-b) & =3: 7: 9 & s(s-a): s(s-b): s(s-c)=3: 7: 9 & (s-a):(s-b):(s-c)=3: 7: 9 aligned So, we have: aligned & s-a=3 k a+b+c-a 2 =3 k b+c-a=6 k ...(1) & and s-b=7 k a+c-b=14 k ...(2) & s-c=9 k a+b-c=18 k ...(3) aligned Solving equation (1), (2) and (3), we get: aligned & a=16 k, b=12 k, c=10 k & a: b: c=16: 12: 10=8: 6: 5 aligned

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