In the figure below, the angle POQ is 90 degrees. What is the perimeter of the triangle OPQ ? 

Solution: 

 অনুবাদঃ POQ একটি সমকোণী ত্রিভুজ । ত্রিভুজটির পরিসীমা বের করতে হবে । 

    (x₁ , y₁ ) এবং (x₂  , y₂ ) 

   দূরত্ব = \(\sqrt {{{({x_1} - {x_2})}^2} + {{({y_1} - {y_2})}^2}} \) 

    PO = \(\sqrt {{{( - 4 - 0)}^2} + {{(4 - 0)}^2}}  = \sqrt {16 + 16}  = \sqrt {32} \) 

        = \(\sqrt {2 \times 16}  = 4\sqrt 2 \) 

  QO = \(\sqrt {{{(2 - 0)}^2} + {{(2 - 0)}^2}}  = \sqrt {{2^{2\;}} + {2^{2\;}}} \) 

        = \(\sqrt {2 + {2^{2\;}}}  = 2\sqrt 2 \) 

  PO = \(\sqrt {{{( - 4 - 2)}^2} + {{(4 - 2)}^2}}  = \sqrt {{{( - 6)}^2} + {{(2)}^2}} \)

       = \(\sqrt {40}  =  = 2\sqrt {10} \) 

      Perimeter of OPQ will be = \((4\sqrt 2  + 2\sqrt 2  + 2\sqrt {10} )\) 

                                          = 6\(\sqrt 2 \) + 2\(\sqrt {10} \)