A Fun Maths Challenge

[Lster]

Hi everyone (and especially those into maths)

Here is a problem I was asked today as an extra challenge in computer science (although it is purely mathematical). I have now solved it with a program I wrote and some algebra, but I am very interested in other peoples methods and solutions. I will post my method straight after the first person solves it! (Please note that this isn't homework of any kind - just a fun puzzle. :))

I've made a diagram showing everything marked out but I'll describe it here. There is a wall with a crate against it (side length 4 units). A 20 unit ladder leans against the crate, touching the corner of the crate, the wall and the floor. x is the distance from the end of the crate to the beginning of the ladder (on the floor) and is what you must find!

Good luck and have fun. :)
Lster

[mips]

I'm to old to remember geometry but it does not look to hard, it's a combo of algebra & geometry.

Bottom = 4+x
Side = 4+y (just label the part above the crate y)
20 = this is the part my brain forgot but it will involve the above two

Now just solve x :)

[Lster]

Yes, that's what I did first. Do you mean use Pythagoras's Theorem next?

[SomeGuyDude]

Mathwise we'd have... sqrt((4+y)^2) + (4+x)^2) = 20, but I'm a little baffled as to where to go from here. Gimme 15 minutes and I might have something.

[aimran]

Haha! Nice try trying to trick us into doing your homework!

[PriceChild]

Mathwise we'd have... sqrt((4+y)^2) + (4+x)^2) = 20, but I'm a little baffled as to where to go from here. Gimme 15 minutes and I might have something.What is y in terms of x? (notice "similar triangles") then solve for x. mmmmm easy ;)

[GeneralZod]

Mathwise we'd have... sqrt((4+y)^2) + (4+x)^2) = 20, but I'm a little baffled as to where to go from here. Gimme 15 minutes and I might have something.

Hint: There is more than one triangle where all three sides can be expressed in terms of x & y.

Edit:

Aaargh - Pricechild's is much better! Damn, I'm rusty :)

[mips]

Yes, that's what I did first. Do you mean use Pythagoras's Theorem next?

yes, thats the guy.

[Lostincyberspace]

12

[Lster]

12

I didn't make it that. I may well be wrong but post a quick solution. I will post mine now as well. :)

[Lster]

...Now removed my method...

[PriceChild]

I got the same quartic. I think you're cheating by using a program to do the final bit for you ;)

I just went through mine on paper... then realised I must have made a silly error somewhere so its back to the start *grr*

[PriceChild]

By the way you're missing a solution.

Don't let the diagram fool you into thinking that x > 16/x

[Lster]

By the way you're missing a solution.

Don't let the diagram fool you into thinking that x > 16/x

I didn't say that did I? :)

[Lster]

I just included one solution.

[Lostincyberspace]

I was guessing not bad though for a guess.

[Lster]

Yes, it seems it was a good guess! :)

[DeusEx]

try relating the three triangles by introducing y, z_1 and a z_2 where:

z_1 + z_2 = 20

and y is the equivalent to x for the wall.

This will result in three equations with three variables, should be solved quite easily.