Ladder problem: Two hallways meet at right angles....

[jwpaine]

Hello,

This is a problem that I am working on from my Spivak calculus book: I'll be very upset if someone gives me too big of a hint.

Two hallways, of width a and b, meet at right angles. What is the greatest possible length of a ladder which can be carried horizontally around the corner?

_______________
|                 |
|            /    b
|          /      |
|        /_______
|      /  |
|    /    |
|  /      |
|/        |
| --a--

I will be needing to create an equation which I will then find the max of using differentiation techniques. Obviously creating the equation is going to be the hardest part -

Can I just have a "hint" on what I should do to move forward?

Some things that I was thinking:

1> Letting the ladder be a line with end points P and Q touching the walls... some how use the distance formula

2> maximizing the area created by the ladder and the walls

I'm not sure what tools I would use to get started

Any small hints would be greatly appreachiated

 

[galactus]

See here:

http://www.mathhelpforum.com/math-help/ ... ation.html


Just use a and b instead of integers and derive the general formula.

It is given in the post, but try deriving it yourself.

 

[jwpaine]

Thanks