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NTSE Sample Paper NTSE SAT Practice Test-9

  • question_answer
    If the hypotenuse of a right angled triangle is 41 cm and the area of the triangle is 180 \[c{{m}^{2}}\], then the difference between the lengths of the legs of the triangle must be

    A) 22 cm     

    B)        25 cm

    C) 27cm                           

    D) 31 cm

    Correct Answer: D

    Solution :

    [d] \[{{a}^{2}}+{{b}^{2}}=\text{ }{{\left( 41 \right)}^{2}}\text{ }and\text{ }\frac{1}{2}\text{ }ab=180\] \[\Rightarrow {{a}^{2}}+{{b}^{2}}=1681\]and \[ab=360\] \[{{\left( \text{a}-b \right)}^{2}}={{a}^{2}}+{{b}^{2}}-\text{ 2}ab\] \[=1681-720=961\] \[\therefore \text{ }a-b=31.\]


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