Manisha and Sandeep started moving from the same point in North and East direction respectively. Manisha got tired after some time. She talked to Sandeep on phone and came to know that he has travelled 2 k.m. more than her. If distance between them at that very moment is 10 km, then find the distances travelled by them separately



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Let Manisha travelled x km
then, sandeep travelled (x+2) km
as we know, north and east direction is perpendicular to each other.
so, by Pythagoras' theorem,
x² + (x+2)² =10²
⇒x² + x² +4+ 4x =100
⇒x² +2x -48=0
⇒x²+ 8x -6x -48=0
⇒x(x+8) -6(x -8)=0
⇒(x+8)(x-6) =0
⇒x = -8 or 6
distance can't be negative , so x =6
hence manisha travelled 6 km and manish travelled 8 km