# Optimization Fence Problem

1calculus1

## Homework Statement

An eight-foot fence stands on level ground is one foot from a telephone pole. Find the shortest ladder that will reach over the fence to the pole.

Pythagoras?
Derivative.

## The Attempt at a Solution

The problem is I don't know how to start this equation due to the fact that it does not have an equation to work with. You see, I'm used to seeing an equation with these kind of question then all I have to do is get the Pythagoras of the picture (telephone pole to the over the fence). Then after that I eliminate 1 variable from the 2 variable equation then use the resulting equation to get its derivative. From the derivative, I can get an x or y value depending on which I had eliminated first from the previous step before getting the derivative. Then plug that in from my original equation and get a point.

Homework Helper
You can draw a picture of the situation, yes? Now put numbers where you know the distance and label the distances you don't know with variables. I would suggest e.g. you call the height where the ladder touches the pole h and the distance to the fence x. You have two similar triangles. Can you use that to express h in terms of x? Now write an equation for the length of the ladder and maximize it in terms of the single remaining variable.

1calculus1
OH, THANK YOU!
Problem solved. =)