Spot on the Table
A boy, recently got home from school, wished to give his father an exhibition of his precocity. He pushed a large circlular table into the corner of the room, so that it touched both walls, and he then pointed to a spot of ink on the extreme edge.
"Here is a little puzzle for you, father," said the youth. "That spot is exactly 8 inches from one wall and 9 inches from the other. Can you tell me the diameter of the table without measuring it?"
- Eric again
"Here is a little puzzle for you, father," said the youth. "That spot is exactly 8 inches from one wall and 9 inches from the other. Can you tell me the diameter of the table without measuring it?"
- Eric again
Labels: SharedPuzzle
posted by Mr Fahrenheit at
4:55 PM
18 Comments:
This is a complicated one cause it doesn't seem to come out even. But the equation I used was
Circumference = pi * D or
The approx circumference is 68 (8+9)*4
and pi is 3.14
ssoooo 68=3.14
divide 3.14 from both sides and you get 21.66 roughly.
as a "test to see if that's correct you multiply 21.66*3.14 with equals
68.0124
YIKES!
So yea... that's all I got and I ain't gotz no more...
The answers just roughly
21.66
D= Diameter btw...
another mistake...
21.66 Inches....
Not sure how the kid finds that a large table but yea....
I get a diameter of either 10 inches (spot is on the outside) or 58 inches (spot is on the inside). That makes the table either pretty small or pretty big. I won't explain how I got there, it would take too long.
actually, it won't take to long.
The math is
' r = x + 9
^ r = y + 8
^ x² = r² - y²
' r = (r²-y²)^(1/2) + 9
^ y = r - 8
r = (r²-(r-8)²)^(1/2) +9
r = (16r-64)^(1/2) + 9
(r-9)² = 16r - 64
r² - 18r + 81 = 16r -64
r² - 34r + 145 = 0
(r-17)² - 12² = 0
r = 5 or r = 29
d=2r => d=10 or d=58
Good answers, but both of you are wrong I'll give the answer when i get back from school
from a standard circle equ
(x - h)^2 + (y - k)^2 = R^2
R^2 = (8 - R)^2 + (9 - R)^2 = R^2
R^2 = (R^2 - 16R + 64) + (R^2 - 18R + 81)
R^2 = 2R^2 - 34R + 145
0 = R^2 - 34R +145
0 = (R - 29)(R - 5)
R = 29 or 5
the diameter is most likely 59 inches because 10 would be a small table
sorry 58 hit the wrong key
Wow, you guys all had a too complicated, there is a simpiler way, Double the product of the 2 distances from the walls. This gives you 144, which is the square of 12. The sum of the two distances is 17. If we add these two numhers, togother and also subtract one from the other, we get the two answers: either 29 or the radius, which means that the diameter was 8 or 10in.
Where are you getting the 17 out of curiosity?
I don't really see how that is a circle equation though... I mean mine was the simplest circle equation in any math book I've had (just doesn't look simple when all typed out XD)
Eric, I'll hand it to you, your method is more elegant than ours (anonymous's and mine), but that doesn't mean ours were wrong. We got to the right answer without too much fuss (I'm presuming you have a typo, you meant to say "...the diameter was [i]58[/i] or 10in", which is what you get using your method, too). Also, I would be interested as to whether you can explain [i]why[/i] your method leads to the right answer.
Damn, Keep getting the HTML wrong.
how do you do that type of math?
There is nothing to it It is simple the answer is a table doesnt have an edge
LOLOLOLOLOLOLOL HAHAHAHAHAHAHAHAHAHAHA nerds................lol
Eric, please explain your work. It looks to be about 6 calculation steps either way, so I'm not sure one is much harder than the other. I got the answer using the geometry/quadratic method. I'm not sure why your works, and I'd love to hear your explanation. Thanks.
I mean conceptually, of course. I understand that the two methods reduce to the same equations. Yours are simpler, but the math to derive yours from the quadratic equations are not so simple.
I get rid of my previous comment asking about the 17... I went dyslexic for a moment and didn't see that it says "sum" right there :P
34 or 8 1/2
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