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NTSE Sample Paper NTSE SAT Practice Test-15

  • question_answer
      The perimeter of a triangle is 30 cm and its area is 30 cm2. If the largest side measures 13 cm, then the length of the smallest side is            

    A) 3 cm                            

    B) 4 cm                  

    C)      5 cm      

    D) 6 cm          

    Correct Answer: C

    Solution :

    [c] Let x be the length of the smallest side, then the other sides are 13 cm and \[\left( 17-x \right)\]cm. s = 15 (semi-perimeter) \[\Delta \,\,=\,\sqrt{s\,(s-a)(s-b)(s-c)}\] \[{{30}^{2}}=15\times \left( 15-13 \right)\left( 15-x \right)\left( 15-17+x \right)\] \[900=15\times 2\times \left( 15-x \right)\left( x-2 \right)\] Which gives x = 5 or 12 \[\therefore \] smallest side = 5 cm.                      


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