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A pole has to be erected …

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A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres is it possible to do so if yes at what distances from the two gates should the pole be erected

    • Posted by Aachal Singh 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

    Let P be the position of the pole and A & B be the opposite fixed gates.  Let, BP= x metres.
    {tex}\therefore{/tex} AP = x + 7
    In right triangle APB, 
    AP2 + BP2 = AB2
    {tex}\Rightarrow{/tex}(x + 7)2 + x2 = 132
    {tex}\Rightarrow{/tex}x2 + 49 + 14x + x2 = 169
    {tex}\Rightarrow{/tex} 2x2 + 14x + 49 - 169 = 0
    {tex}\Rightarrow{/tex}2x2 + 14x - 120 = 0
     {tex}\Rightarrow{/tex}2(x2 + 7x - 60) = 0
    {tex}\Rightarrow{/tex} x2 + 7x - 60 = 0
    {tex}\Rightarrow{/tex}x2 + 12x - 5x - 60 = 0
    {tex}\Rightarrow{/tex} x(x + 12) - 5(x + 12) = 0
    {tex}\Rightarrow{/tex} (x + 12)(x - 5) = 0

    {tex}\Rightarrow x=5 \ or \ -12{/tex}

    As x can not be negative. So, x = 5. 

    Therefore, AP = 7+5 = 12
    Hence, AP = 12 m and BP = 5 m

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