area of a triangle??

[credit_vixen]

I can't figure this out, do you think you guys can help me?

Two sides of a triangle are given as 'a' and 'b'. What is the largest area the triangle can have?

Answers must be in terms of 'a' and 'b'.
NO OTHER VARIABLES SHOULD BE IN THE ANSWER!


what do you guys and girlz think?

[brutfood]

My mathematical intuition tells me ab/2. So I'm going to post it up here, and see if it gets shot down in flames. I've assumed maximum area for right angle case, and that if a and b represent the two shortest sides, you will get the maximum area.

[brutfood]

Ok, just proved it mathematically. It boiled down to a:-

a.b.sin(theta)/2. (maybe they taught me this at school? - must have missed that day - but derived it from scratch ok).

And sin(theta) has a maximum value of 1.

Hence ab/2

[credit_vixen]

looks like you guys are both right!
you rule!

[brutfood]

There's only one of me But two sides of my brain. The right side visualises the problem, and intuatively has a feel for the solution - but this is never enough for the cynical doubting language and fact and symbol oriented left hemisphere, and it always demands proof! (Waste of time usually)

If you enjoyed my solution, please check out my work in progress, and give me some feedback

http://au.geocities.com/brutfood/


Cheers, Daniel (Alias Brutfood)