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MHT CET20244 May 2024Evening ShiftMathematicsProperties of TrianglesActual

If ( a + b ) C +( b + c ) A +( c + a ) B =72 and if a =18, ~b =24 , then area of the triangle ABC is

Options

  1. A144 sq.units
  2. B216 sq.units
  3. C256 sq.units
  4. D296 sq.units

Correct answer

B. 216 sq.units

Step-by-step solution

aligned &(a+b) C+(b+c) A+(c+a) B=72 & a C+b C+b A+c A &+c B+a B=72 & a C+c A+b A+a B &+b C+c B=72 aligned [ array l By projection a=b C+c B b=c A+a C c=a B+b A array ] aligned & b + c + a =72 & a + b + c =72 & aligned & 18+24+ c =72 [ a =18, ~b =24 . Given ] & c =30 aligned & aligned Area of ABC & = s ( s - a )( s - b )( s - c ) & = 36(36-18)(36-24)(36-30) & = 36 18 12 6 & =216 sq. units aligned aligned

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