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NIELIT 2017 DEC Scientist B - Section A-47

If $10$, $12$ and '$x$' are sides of an acute angled triangle, how many integer values of '$x$' are possible?

  1. $7$
  2. $12$
  3. $9$
  4. $13$
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Option C. 9

Acute Angle : between 0 and 89 degrees.

Case 1: X is the longest side

then X < $\sqrt{10^{2}+12^{2}}$ i.e. X < 16

Case 2: 12 is the longest side.

then X >  $\sqrt{12^{2}-10^{2}}$  i.e.  X > 6

Therefore x ranges from 7 to 15 = 9 Values

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