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Manipal MET2014MathematicsProperties of Triangles

In a triangle, the lengths of two larger sides are 10 cm and 9 cr. . If the angles of the triangle are in AP , then the length of the third side is

Options

  1. A5 - 6
  2. B5 - 6
  3. C5 6
  4. D5 6

Correct answer

D. 5 6

Step-by-step solution

Let in the figure, A B C Angles are in A.P. array ll & C= -d, B= and & A= +d array As A+ B+ C=180^ array rrrl & +d+ + -d & =180^ & 3 & =180^ & & & =60^ array Now in A B C , aligned B & = a^2+c^2-b^2 2 a c 60^ & = (10)^2+x^2-9^2 2 10 x 1 2 & = 100+x^2-9^2 20 x x^2-10 x+19 & =0 x & = 10 100-76 2 & = 10 24 2 =5 6 aligned

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