What Is The Length Of The Shortest Ladder That Cou

Anonymous

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What is the length of the shortest ladder that could lean against the box (toufhing point (2,1)) and rest on the ground (x axis) and against the wall (y axis)? Find the equation of the line segment that represent the ladder.

 

Answer No.1

ComputerSupa

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Let the ladder touch X axis at a and Y axis at b. So, the equation of the line is x/a + y/b = 1 It passes through (2,1) So, 2/a + 1/ b = 1 a = 2b/(b-1) Length of ladder = √(a^2 + b^2) For minimum length,its derivative must be '0' So, dl/db = 0 (1/√(a^2 + b^2)) (2a da/db) + 2b = 0 a da/db = -b (-2/(b-1)^2)*(2b/(b-1)) = -b Solving, we get b = (2)^1/3 +1 a = 2 + (4)^1/3

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