Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

Post a reply

Go back

Write your message and submit
:) :| :( :D :o ;) :/ :P :lol: :mad: :rolleyes: :cool: | :dizzy :eek :kiss :roflol :rolleyes :shame :down :up :touched :sleep :wave :swear :tongue :what :faint :dunno
Options

Go back

Topic review (newest first)

bobbym
2013-06-01 22:27:38

Hi;

That is very good. Nice work.

ElainaVW
2013-06-01 22:23:32

[Code fixed by admin]

Code:

Solve[{12 ==1/a Sqrt[2] \[Sqrt]((a + b + c) (1/2 (a + b + c) - a) (1/2 (a + b + c) - b) (1/2 (a + b + c) - c)), 14 == 1/b Sqrt[2] \[Sqrt]((a + b + c) (1/2 (a + b + c) - a) (1/2 (a + b + c) - b) (1/2 (a + b + c) - c)), 
   83 == 1/c Sqrt[2] \[Sqrt]((a + b + c) (1/2 (a + b + c) - a) (1/2 (a + b + c) - b) (1/2 (a + b + c) - c)), 12 == (b*c)/(2 R)}, {a, b, c, R}] // N

Only had to try 84 and 83.

bobbym
2013-06-01 22:20:44

Hi;

What is it, please post what you have.

ElainaVW
2013-06-01 22:19:55

I have a different solution.

anonimnystefy
2013-05-31 05:17:45

Okay, see you! smile

bobbym
2013-05-31 05:02:38

Hi;

Okay, see you later.

anonimnystefy
2013-05-31 04:58:27

Well, it is because a*ha=b*hb=c*hc. From this we can get a:b:c=(1/ha):(1/hb):(1/hc), which means that, if a, b and c can form a triangle, 1/ha, 1/hb and 1/hc must be able to form a triangle as well.

bobbym
2013-05-31 04:54:38

I do not get it but it works so the problem is done.

anonimnystefy
2013-05-31 04:47:46

Yes, but, as I already said, 1/ha=1/12, 1/hb=1/14 and 1/hc must be length of some triangle in order to be a valid set of altitudes.

bobbym
2013-05-31 04:46:32

What triangle? That inequality is for the sides. You have altitudes there.

anonimnystefy
2013-05-31 04:44:31

The triangle inequality states that 1/hc+1/14>1/12.

bobbym
2013-05-31 04:41:33

Why the minus and not a plus?

anonimnystefy
2013-05-31 04:40:26

What about it?

bobbym
2013-05-31 04:38:33

Okay but what about this?

1/hc>1/12-1/14

anonimnystefy
2013-05-31 04:32:01

Well, I had the fact that the lengths 1/12, 1/14 and 1/hc must form a triangle, where 1/hc is as small as possible. Because of the triangle inequality we have that 1/hc>1/12-1/14=1/84. So, hc<84. The maximum possible length is 83.

Board footer

Powered by FluxBB