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Calculus/Optimization problem...

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Expert: - 4/18/2008


Question
In this question it says:

A fence 8ft tall runs parallel to a tall building at a distance of 4 ft 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.

I believe this  has something to do with the law of similar triangles, but I really dont know where to start with this.

Answer
The fence is 8ft tall and 4 from the building.

Construct a triangle with some base y between the ladder and the fence.  The ladder will reach the building at some height x.

It is known that 8/y (the two legs on the ladder triangle) is the same as x/(4+y) (the two legs on the similar, bigger triangle).

Set both equal to each other and solve for y.

Now note that what we are trying to minimize is the length of the ladder.  That is given by ((4+y)^2+x^2)^0.5.

To solve this, you can solve for y and put it into the equation.  Once this has been done, take the derivative.

The answer is somewhere between 10 and 20 feet of ladder.

Finish the details of solving this question.  If more help is needed, please write again.  Have a good day!  

Calculus

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