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AP EAMCET201824 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

In A B C , if s-a 11 = s-b 12 = s-c 13 , then ^2 ( A 2 )+ ^2 ( C 2 )=

Options

  1. A290 429
  2. B290 143
  3. C143 33
  4. D113 33

Correct answer

A. 290 429

Step-by-step solution

Given that, s-a 11 = s-b 12 = s-c 13 =k aligned & s-a=11 k & s-b=12 k & s-c=13 k aligned On adding, aligned 3 s-(a+b+c) & =36 k 3 s-2 s & =36 k s & =36 k aligned [ as a+b+c=2 s] Now, ^2 A 2 + ^2 C 2 aligned & = (s-b)(s-c) s(s-a) + (s-a)(s-b) s(s-c) & = (12 k)(13 k) (36 k)(11 k) + (11 k)(12 k) (36 k)(13 k) = 12 36 [ 13 11 + 11 13 ] & = 1 3 [ 169+121 11 13 ]= 290 429 aligned

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