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 Ladders Without Snakes (Posted on 2003-04-21)
There is a 6 metres wide alley. Both walls of the alley are perpendicular to the ground. Two ladders, one 10 metres long, the other 12 metres, are propped up from opposite corners to the adjacent wall, forming an X shape. All four feet of each ladder are firmly touching either the corner or the wall. The two ladders are also touching each other at the intersection of the X shape.

What is the distance from the point of intersection from the ground?

 Submitted by Ravi Raja Rating: 2.8571 (7 votes) Solution: (Hide) Let us consider the foot of one of the ladders as the origin. The width of the alley is given to be equal to 6. Thus if we consider the alley to be the axis of x and the wall from the origin (as assumed) to be the axis of y, then the coordinates of the four feet of the two ladders are: (0,0),(6,8) for the First Ladder and (6,0),{0,(108)^(1/2)} for the Second Ladder. Now the equation of the two ladders are: y = (4/3)x and y = -{(3)^(1/2)}x + (108)^(1/2) Solving the two equations, we get: y = 4.52 (approximately) which is the required height.

 Subject Author Date answer K Sengupta 2007-11-23 23:35:31 Excel solution Jim 2004-10-04 11:11:33 Using similar triangles Nick Hobson 2004-06-13 12:08:42 Pull the trigger Jack Squat 2004-01-16 15:03:52 my solution DuCk 2003-04-22 05:38:11 solution annij 2003-04-21 17:24:28 re(2): solution Charlie 2003-04-21 09:23:22 re: solution Bryan 2003-04-21 09:12:45 Interesting problem jude 2003-04-21 09:05:33 solution Charlie 2003-04-21 09:01:01

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