Uttarakhand Government accomplished a Golden Triangular Project. Under this Project, the State Government Laid down 6 lane roads connecting the three cities Dehradun, Haridwar and Rishikesh which are equally separated from each other i.e., in terms of the Geometry they form an equilateral triangle. Ram and Shyam start simultaneously from Dehradun and Haridwar respectively, towards Rishikesh. When Ram covers 20km, Shyam covers such a distance that the distance between Ram and Shyam makes 90°angle with the road joining Haridwar and Rishikesh. When Shyam reaches Rishikesh, Ram is still 30 km away from Rishikesh. Find the distance between Dehradun and Haridwar?
(20+x/2)/20= (20+x)/((20+x-30)) (40+x)/40= (20+x )/(x-10) 40x+x²-10x-400=800+40x x²-10x-1200=0 x²-40x+30x-1200=0 x(x-40)+ 30(x-40)= 0 x=40,-30 The distance between Dehradun and Haridwar is 40 +20 = 60km (since Distances of Dehradun, Haridwar and Rishikesh are equal).
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