ok all you smarty smarts...answer this simple math/geometry question

[pokerfan]

One of my personal favorite puzzles. No fair googling.

Two ladders of lengths a = 40 and b = 30 feet are propped in an alley, as shown. The ladders cross each other at a height of h = 12 feet above the alley floor. What is the width of the alley?

[mainegreen]

1. I hate you.

Now I have to work on this.
x(

[pokerfan]

4. Bumping for the math geeks

[pintobean]

2. I believe this is

an OSHA violation. The proper lean ratio is 4 to 1. Not only that, it's out of focus.

[pokerfan]

3. LOL

[Redstone]

5. Just wide enough to have another drink in.

Redstone

[hellbound-liberal]

6. You're going to have to give me some time to think about this

Please don't post the answer before 5:00 PM today. I'll have my answer by then. Maybe.

[meegbear]

7. ...

21 feet

[pokerfan]

8. Nope

It's not an integer.

[commander bunnypants]

9. 47

CB

[wildhorses]

10. the answer is 42

always;)

[commander bunnypants]

11. I thought it was 47

danks

CB

[wildhorses]

12. of course 69 is always a good solution --

:evilgrin:

:hi:

[hellbound-liberal]

13. I give up, Pokerfan. Is this figure drawn to scale?

[pokerfan]

14. Not drawn to scale, but the answer is

there is no answer. Well, of course there is an "answer," but it can not be solved directly.

It looks like it should be relatively easy but devolves into algebraic hell:

B^4-2hB^3+B^2(a^2-b^2)-2hB(a^2-b^2)+c^2(a^2-b^2)=0

Solving a 4th degree equation is a little difficult. But if you can solve the above equation for B, then you can easily deduce w using the Pythagorean Theorem.

Wikipedia has a pretty good entry on the problem: http://en.wikipedia.org/wiki/Crossed_Ladders_Problem

I like to spring it on engineering candidates just to torture them and get some insight on how they go about the problem solving process.

[MikeH]

16. B = very close to 19, w = a little over 23.2 feet

I was trying this out.

For a = 40, b = 30, h = 12, the above formula works to

B^4 - 24*B^3 + 700*B^2 - 16800*B + 100800 = 0

which can also be written (for ease of calculation) as

(((B-24)B+700)B-16800)B+100800

Looking at the geometry, one would see that B > 12 (h) and B < 30 (b).

It turns out that B=19 gives the value 5 for the above expression, which is very, very close given the large coefficients and large values of the powers; the true value of B is just very, very slightly less than 19.

This gives w = approximately the square root of 900 - 361 = 539, or slightly over 23.2 feet.

[Rabrrrrrr]

15. The answer depends on A and B - I'd give you a complex formula,

but quite honestly I don't feel like doing that.

But I do know that, given the data you've given, the answer can only be expressed in terms of A and B, and it'll be a big, beautiful (ugly to non-math-geeks, but they don't count as human beings, so I ignore them) equation.

[KitchenWitch]

17. Oh sweet zombie jesus - you are evil!

x(