Geometry Brain Teaser: Part 2. This time, it's not homework.

[Kyteland]

Inspired by the other thread with the guy trying to get us to do his homework.

• 
  Problem:
  There is a rectangular room that is 16x9. In that room is a rectangular carpet which has a width of 3 and an unknown length. Each of the four corners of the carpet touches a different wall. What is the length of the carpet?
  
  Picture of the problem.

This was our extra credit assignment in my geometry class 8 years ago. It is very much harder to solve than it looks. I was the only person to solve it that year.

*pats self on back*

 

[PlatinumGold]

nope. still not right. i'm making it too hard.

 

[Kyteland]

Originally posted by: PlatinumGold
oops

I'm sorry, but that answer isn't in proper mathematical format. I award you no points.

 

[RaynorWolfcastle]

ummm... this is an easy pythagoras problem, give me a min and I'll have it done for you

I get 15.5 units but I did it really quickly and may have made a math mistake somewhere in my calculations

 

[mugs]

:cookie;

 

[Kyteland]

Originally posted by: mugsywwiii
:cookie;

:beer:

You know, for the cookie.

 

[Kyteland]

Originally posted by: RaynorWolfcastle
ummm... this is an easy pythagoras problem, give me a min and I'll have it done for you

I get 15.5 units but I did it really quickly and may have made a math mistake somewhere in my calculations

Yes you did. That is not the answer.

The most common problem when trying to solve this is that everythings cancels out. Every time you set up a system to solve you end up getting 1=1.

 

[bandana163]

The very beginning:
The problem is: geometry1.jpg

Edit: I can't type several symbols right.

 

[PlatinumGold]

((9/25)9)^2 + ((16/25)9)^2 = 9

 

[CPA]

Originally posted by: Vaerilis
The very beginning:
The problem is: geometry1.jpg
Basically:
(16-Y)?2+(9-X)?2 = Needed_line?2

Now the only thing left is what's X and Y.

That's what I was thinking.

 

[Crypticburn]

Originally posted by: PlatinumGold
((9/25)9)^2 + ((16/25)9)^2 = 9

Very good, 1=1!

try this one:

x = 16sec(t)-3*tan(t)
x = 9csc(t)-3cot(t)

where x is the length of the rug, and t is the angle the length makes with the wall of length 16.

Crypticburn

 

[PlatinumGold]

Originally posted by: Crypticburn

Originally posted by: PlatinumGold
((9/25)9)^2 + ((16/25)9)^2 = 9

Very good, 1=1!

try this one:

x = 16sec(t)-3*tan(t)
x = 9csc(t)-3cot(t)

where x is the length of the rug, and t is the angle the length makes with the wall of length 16.

Crypticburn

the square root of ((9/25)9^2) = short length of small triangle.

etc etc

 

[ZeroNine8]

42

 

[FuzzyBee]

i get 15.87 ft.

x^2 + y^2 = 3^2

x/y = 9/16

x ~= 2.61'
y ~= 1.47'

(16-y)^2 + (9-x)^2 = length ^2

211.1209 + 40.8321 = length^2

 

[Kyteland]

Originally posted by: PlatinumGold
((9/25)9)^2 + ((16/25)9)^2 = 9

That doesn't seem to work for me.

((9/25)9)^2 = (81/25)^2 = 10.4976
((16/25)9)^2 = (144/25)^2 = 33.1776

((9/25)9)^2 + ((16/25)9)^2 != 9

Your other post suggests you meant this
(9/25)(9^2) + (16/25)(9^2) = 9 but that also isn't right

Can you clarify what you were typing?

 

[RaynorWolfcastle]

OK, I'll post up the method in a pic so that those who don't want to be given the answer don't see it, give me a min to draw it up in paint

 

[Kyteland]

Originally posted by: fuzzy bee
i get 15.87 ft.

x^2 + y^2 = 3^2

agreed

x/y = 9/16

By what property do you get this? I would agree that x/y=(16-y)/(9-x), but that I do not agree with.

x ~= 2.61'
y ~= 1.47'

(16-y)^2 + (9-x)^2 = length ^2

211.1209 + 40.8321 = length^2

 

[dxkj]

14.3 feet?

 

[Kyteland]

Originally posted by: dxkj
14.3 feet?

I don't actually remember the answer. I may have to go home and look it up during lunch. I seem to remember it being 13.something, but it was eight years ago so.....

 

[RaynorWolfcastle]

Originally posted by: Kyteland

Originally posted by: dxkj
14.3 feet?

I don't actually remember the answer. I may have to go home and look it up during lunch. I seem to remember it being 13.something, but it was eight years ago so.....

I put the method up, the answer is kind of irrelevant


WRONG ANSWER - only works for square rooms

 

[Kyteland]

Originally posted by: RaynorWolfcastle

Originally posted by: Kyteland

Originally posted by: dxkj
14.3 feet?

I don't actually remember the answer. I may have to go home and look it up during lunch. I seem to remember it being 13.something, but it was eight years ago so.....

I put the method up, the answer is kind of irrelevant
ANSWER - WARNING

That assumes that the third angle in that triangle is a right angle. It is not.

Also, I just pulled out my original of the question, and the long side is 12, not 16. I'll quick redo the math for 16 and see what I get.

 

[RaynorWolfcastle]

Ummm... yes it is, it's just that my drawing sucks. The cross line is parallel to the edges of the carpet, unless I'm missing something.

edit: Your carpet *is* going straight across the room, right?

 

[Kyteland]

Originally posted by: RaynorWolfcastle
Ummm... yes it is, it's just that my drawing sucks. The cross line is parallel to the edges of the carpet, unless I'm missing something.

edit: Your carpet *is* going straight across the room, right?

No. Your line will cut the carpet in to 2 exactly equal pieces, but those pieces will not be rectangles. They will only be trapezoids.

 

[jwells777]

Hmm....perhaps I am missing something...seems straightforward....3 equations...3 unknowns....non-linear....solve

 

[Kyteland]

Originally posted by: RaynorWolfcastle
Ummm... yes it is, it's just that my drawing sucks. The cross line is parallel to the edges of the carpet, unless I'm missing something.

edit: Your carpet *is* going straight across the room, right?

No. Your line will cut the carpet in to 2 exactly equal pieces, but those pieces will not be rectangles. They will only be trapezoids.

Edit: In you picture, if you do all of the math you end up with x=6, y=8. This means that the smaller triangle has sides 3 and 8. That is obviously wrong.

The triangle formed by cutting the 16x9 rectangle from corner to corner is not similar to the triangle formed by the rug.

From an earlier post:

x/y = 9/16

By what property do you get this? I would agree that x/y=(16-y)/(9-x), but that I do not agree with.