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MHT CET202124 Sep 2021Morning ShiftMathematicsProperties of TrianglesActual

The area of the triangle ABC is 10 3 ~cm ^2 , angle B is 60^ and its perimeter is 20 ~cm , then ( AC )=

Options

  1. A10 cm
  2. B8 cm
  3. C5 cm
  4. D7 cm

Correct answer

D. 7 cm

Step-by-step solution

aligned & Area = acsin B 2 = 10 3 = acsin 60^ 2 & 10 3 = a c 3 4 a c=40 aligned Now aligned & B= a^2+c^2-b^2 2 a c & 60^ 2 a c=a^2+c^2-b^2 & 1 2 2 40= (a^2+c^2 )-2 a c-b^2 & 40=(20-b)^2-(2 40)-b^2 [a+b+c=20, given ] & =400+b^2-40 b-80-b^2 & 40 b=280 b=7 aligned

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