Maths-
General
Easy

Question

Three straight lines are drawn through a point M, lying in the interior of triangle ABC, parallel to its sides. The areas of the resulting three triangles are S1, S2 and S3. The area of triangle ABC is

  1. S subscript 1 end subscript plus S subscript 2 end subscript plus S subscript 3 end subscript    
  2. open parentheses square root of S subscript 1 end subscript end root plus square root of S subscript 2 end subscript end root plus square root of S subscript 3 end subscript end root close parentheses to the power of 2 end exponent    
  3. fraction numerator open parentheses S subscript 1 end subscript plus S subscript 2 end subscript plus 5 subscript 3 end subscript close parentheses to the power of 3 divided by 2 end exponent over denominator S subscript 1 end subscript plus 5 subscript 2 end subscript plus 5 subscript 3 end subscript end fraction    
  4. N o n e blank o f blank t h e s e    

The correct answer is: open parentheses square root of S subscript 1 end subscript end root plus square root of S subscript 2 end subscript end root plus square root of S subscript 3 end subscript end root close parentheses to the power of 2 end exponent



    table row cell fraction numerator blank A r e a blank o f blank A B C over denominator blank A r e a blank o f blank P Q M end fraction equals fraction numerator B C to the power of 2 end exponent over denominator Q M to the power of 2 end exponent end fraction end cell row cell fraction numerator blank A r e a blank o f blank A B C over denominator blank A r e a blank o f blank M N P end fraction equals fraction numerator B C to the power of 2 end exponent over denominator N P to the power of 2 end exponent end fraction end cell row cell fraction numerator blank A r e a blank o f blank A B C over denominator blank A r e a blank o f blank M O L end fraction equals fraction numerator B C to the power of 2 end exponent over denominator M L to the power of 2 end exponent end fraction end cell end table
    square root of A r e a blank o f blank capital delta A B C end root equals Q M equals fraction numerator B C square root of S subscript 1 end subscript end root over denominator square root of 5 end fraction
    P M equals fraction numerator B C square root of S subscript 3 end subscript end root over denominator square root of 5 end fraction comma M L equals fraction numerator B C square root of S subscript 2 end subscript end root over denominator square root of 5 end fraction left parenthesis Q M equals B N blank a n d blank M L equalsPC)
    B C equals B C open parentheses fraction numerator square root of S subscript 1 end subscript end root over denominator square root of 5 end fraction plus fraction numerator square root of S subscript 2 end subscript end root over denominator square root of 5 end fraction plus fraction numerator square root of S subscript 3 end subscript end root over denominator square root of 5 end fraction close parentheses
    S equals open parentheses square root of S subscript 1 end subscript end root plus square root of S subscript 2 end subscript end root plus square root of S subscript 2 end subscript end root close parentheses to the power of 2 end exponent blank w h e r e blank S blank i s blank a r e a blank o f blank capital delta A B C

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