Maths-
General
Easy

Question

ΔABC and ΔDEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual notations). a, b, c, and d, e, f satisfy the relation square root of a plus b plus c end root square root of d plus straight e plus straight f end root equals square root of ad plus square root of be plus square root of cf then -

  1. Both the triangles ABC and DEF must be isosceles but not equilateral
  2. Both the triangles ABC and DEF must be equilateral 
  3. Both the triangles ABC and DEF must be similar but may not be congruent
  4. Both the triangle ABC and DEF must be similar

The correct answer is: Both the triangle ABC and DEF must be similar


    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis square root of a d end root plus square root of b e end root plus square root of c f end root right parenthesis squared less or equal than left parenthesis a plus b plus c right parenthesis left parenthesis d plus e plus f right parenthesis end cell row cell not stretchy left right double arrow square root of a d end root plus square root of b e end root plus square root of c f end root less or equal than left parenthesis square root of a plus b plus c end root square root of d plus e plus f end root end cell end table
    thereforethe equality will take place if  straight a over straight d equals straight b over straight e equals straight c over straight f
    thereforetriangle must be similar.

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