10th Class Mathematics Triangles Question Bank Case Based (MCQs) - Triangles

  • question_answer
    Hypotenuse of a right triangle is \[\text{25 cm}\] and out of the remaining two sides, one is longer than the other by \[\text{5 cm}\]. Then the length of the longer side is:

    A) \[20\,cm\]

    B) \[15\,cm\]

    C) \[12.5\,cm\]

    D) \[10\,cm\]

    Correct Answer: A

    Solution :

    Consider the right triangle ABC as shown    below.                                
    Let \[BC=x\,cm,\] then \[AB=(x+5)\,cm.\]
    As ABC is a right triangle, applying       
    Pythagoras theorem, we get.           
    Therefore,    \[625={{x}^{2}}+{{x}^{2}}+10x+25\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,2{{x}^{2}}+10x-600=0\,\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,{{x}^{2}}+5x-300=0\,\]
    Factorizing by splitting the middle term.
    \[\Rightarrow \,\,\,\,\,x(x-20)-15(x+20)=0\Rightarrow x=15,\,x=-20\] As length cannot be negative,
    Therefore,  and .
      Length of the longer side
    So, option [a] is correct.

You need to login to perform this action.
You will be redirected in 3 sec spinner