A 5 foot long pole leans against a wall. The bottom is 3 feet from the wall. How much farther should the bottom be pulled away from the wall so that the top moves the same amount down the wall

Question

anonymous · Answer

The ladder against the wall makes a 3-4-5 triangle.  If you increase the base by one foot and decrease the height of the ladder against the wall by one foot, you still have a 3-4-5 triangle.  

If you saw this in your mind's eye, great.  If not, then there is a way to solve the problem algebraically.  Let x be the amount we will increase the base and also decrease the height of the ladder.  The base is now represented as 3+x and the height of the ladder is now represented as 4-x.  By the Pythagorean Theorem, (3+x)^2 + (4-x)^2 = 5^2.  Solving this equation for x yields solutions of x=0 and x=1.