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MHT CET202519 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

If two sides of a triangle are 3 -2 and 3 +2 units and their included angle is 60^ , then the third side of the triangle is

Options

  1. A15 units
  2. B15 -2 units
  3. C15 +2 units
  4. D15 units

Correct answer

D. 15 units

Step-by-step solution

Given two sides of a triangle as a = 3 - 2 and b = 3 + 2 , with included angle C = 60^ , the third side c is found using the Law of Cosines: c^2 = a^2 + b^2 - 2ab C . Compute a^2 = ( 3 - 2)^2 = 7 - 4 3 , b^2 = ( 3 + 2)^2 = 7 + 4 3 , and ab = ( 3 - 2)( 3 + 2) = -1 . Substitute into the formula with 60^ = 1 2 : c^2 = (7 - 4 3 ) + (7 + 4 3 ) - 2(-1) ( 1 2 ) = 14 + 1 = 15 . Thus, c = 15 . Comparing with the options, the length is 15 units.

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