Posted by sonia on Wednesday, November 21, 2012 at 10:21pm.
A fence 5 feet tall runs parallel to a tall building at a distance of 3 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

calculus  Steve, Thursday, November 22, 2012 at 7:57pm
draw a diagram. If the foot of the ladder is x feet from the fence, and the ladder reaches y feet up the wall, then we have
x/5 = (x+3)/y
y = 5 + 15/x
if the length of the ladder is z,
z^2 = (x+3)^2 + y^2
= (x+3)^2 + (5 + 15/x)^2
z = √((x+3)^2 + (5 + 15/x)^2)
dz/dx = (x+3)(x^375) / <a bunch of nonzero junk>
so, dz/dx=0 at x = 3 or ∛75
z^2 = (3+∛75)^2 + (5+15/∛75)^2
z = 11.19 feet
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