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AP EAMCET20226 Jul 2022Evening ShiftMathematicsProperties of TrianglesActual

In a A B C , if a A=b B , where a b , then A B C is

Options

  1. AObtuse angled triangle
  2. BEquilateral triangle
  3. CAcute angled triangle
  4. DRight angled triangle

Correct answer

D. Right angled triangle

Step-by-step solution

aligned & a A=b B & a ( b^2+c^2-a^2 2 b c )=b ( a^2+c^2-b^2 2 a c ) & a b (b^2+c^2-a^2 )= b a (a^2+c^2-b^2 ) & a^2 (b^2+c^2-a^2 )=b^2 (a^2+c^2-b^2 ) aligned aligned & a^2 b^2+a^2 c^2-a^4=a^2 b^2+b^2 c^2-b^4 & a^4-b^4+b^2 c^2-a^2 c^2=0 & (a^2-b^2 ) (a^2+b^2 )+c^2 (b^2-a^2 )=0 & (a^2-b^2 ) [a^2+b^2-c^2 ]=0 & As (a b), a^2-b^2 0 & a^2+b^2-c^2=0 a^2+b^2=c^2 aligned A B C is a right angled triangle with A B as hypotenuse.

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