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10th Class Mathematics Mensuration Question Bank Mensuration

  • question_answer
    If the sides of an equilateral triangle are given by \[\text{2a}-\text{6}-\text{3},\text{a}-\text{b}+\text{1}\] and\[\text{2a}-\text{2b}-\text{1}\], then the perimeter (in cms) of the triangle is

    A)  6                            

    B)         9  

    C)  12                         

    D)         15

    Correct Answer: B

    Solution :

     Since the triangle is equilateral, therefore \[2a-b-3=a-b+1=2a-2b-1\]                 or            \[(2a-b-3)-(a-b+1)=0\] and   \[(2a-b-3)-(2a-2b-1)=0\] or            \[a-4=0,\,b-2=0\] \[\therefore \]  \[a=4\]  or  \[b=2\] These values give \[2a-b-3=2\times 4-2-3=3,\] so that each side is 3 cm. Perimeter \[=3\times 3=9\text{ }cm.\]


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