Author |
Topic: Minimum Triangle Area (Read 639 times) |
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender: 
Posts: 4489
|
 |
Minimum Triangle Area
« on: Jan 12th, 2004, 3:24pm » |
 Quote  Modify
|
I came across the following puzzle recently.
It looks difficult to solve without some programming.
A triangle with sides a, b, and c has an area A equal to n times its perimeter,
where a, b, c, n, and A are all positive integers.
Also, a = n2 + n1/5
What is the minimum possible value for A?
|
| « Last Edit: Jan 30th, 2004, 4:54pm by ThudnBlunder » |
 IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Minimum Triangle Area
« Reply #1 on: Jan 12th, 2004, 4:01pm » |
Quote Modify
|
Is x also restricted to integers?
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: Minimum Triangle Area
« Reply #2 on: Jan 12th, 2004, 4:24pm » |
Quote Modify
|
Quote:| Is x also restricted to integers? |
|
Iff it is equal to n. 
(Thanks, I will correct that now.)
|
| « Last Edit: Feb 2nd, 2004, 5:58pm by ThudnBlunder » |
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
Sameer
Uberpuzzler
Pie = pi * e
Gender:
Posts: 1261
|
|
Re: Minimum Triangle Area
« Reply #3 on: Jan 30th, 2004, 4:00pm » |
Quote Modify
|
on Jan 12th, 2004, 4:01pm, Icarus wrote:| Is x also restricted to integers? |
|
I don't see any x in the questions?  
|
|
IP Logged |
"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: Minimum Triangle Area
« Reply #4 on: Jan 30th, 2004, 4:53pm » |
Quote Modify
|
Quote:| I don't see any x in the questions? |
|
So my correction was successful then?
Thank you for your positive feedback, Sameer.
(Before Icarus queried it, I think I originally had Also, a = x2 + x1/5)
|
| « Last Edit: Jan 30th, 2004, 10:00pm by ThudnBlunder » |
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
Sameer
Uberpuzzler
Pie = pi * e
Gender:
Posts: 1261
|
|
Re: Minimum Triangle Area
« Reply #5 on: Feb 2nd, 2004, 12:07pm » |
Quote Modify
|
Hee... i spent hours thinking there is something wrong with the problem and then I realised I was considering 'n' as the perimeter all the time keke.. Ok back to board for solving this again!!!
|
|
IP Logged |
"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: Minimum Triangle Area
« Reply #6 on: Feb 2nd, 2004, 3:50pm » |
Quote Modify
|
Perhaps I should remove the posts that deal only with correcting the original problem statement, but then again, T&B has lost too many posts lately without me purposely deleting them! 
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
Sameer
Uberpuzzler
Pie = pi * e
Gender:
Posts: 1261
|
|
Re: Minimum Triangle Area
« Reply #7 on: Feb 25th, 2004, 9:02am » |
Quote Modify
|
Ok so I just approached it with simple trigonometric formulas and came up with this equation and am at stalemate
2nA + (A/2n)*( (A/2n) - (n2+n1/5)2 = bc( (A/2n) - (n2+n1/5))
I don't know where to go from here. Anyone?
Also there can be other method ?
|
|
IP Logged |
"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
|
|
|
aero_guy
Senior Riddler
Gender:
Posts: 513
|
|
Re: Minimum Triangle Area
« Reply #9 on: Mar 8th, 2004, 3:39pm » |
Quote Modify
|
Sameer, also do not forget the limitations on the relative size of a, b, and c. Neither of them can be larger than the sum of the other two.
|
|
IP Logged |
|
|
|
Sameer
Uberpuzzler
Pie = pi * e
Gender:
Posts: 1261
|
|
Re: Minimum Triangle Area
« Reply #10 on: Mar 9th, 2004, 7:52am » |
Quote Modify
|
Hmm I haven't looked at this problem in a while. I shall take a look at it this weekend with Barukh's and aero_guy's hints!!
|
|
IP Logged |
"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print