Let A D and B C be two vertical poles at A and B respectively on a horizontal ground. If A D = 8 m , BC = 11 m , AB = 10 m ; then the distance (in meters) of a point M lying in between AB from the point A such that MD 2 + MC 2 is minimums, is__

Question

Let A D and B C be two vertical poles at A and B respectively on a horizontal ground. If A D = 8 m , BC = 11 m , AB = 10 m ; then the distance (in meters) of a point M lying in between AB from the point A such that MD 2 + MC 2 is minimums, is__,

MARKS App · Accepted Answer

Let AM = x and S = MD 2 + MC 2 So, MD 2 + MC 2 = 64 + x 2 + 121 + ( 10 - x ) 2 ⇒ S = 285 - 20 x + 2 x 2 dS dx = - 20 + 4 x ⇒ dS dx = 0 ⇒ x = 5 d 2 S dx 2 = 4 = + ve

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