In a triangle with sides , , the following holds: . What can be the maximum area?

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- January 9th 2010, 08:09 AMjames_bondTriangle with 0<a<1<b<2<c<3
In a triangle with sides , , the following holds: . What can be the maximum area?

- January 9th 2010, 10:17 AMHenryt999Maximum area
.

- January 9th 2010, 11:19 AMGrandad
- January 9th 2010, 11:23 AMHenryt999Thanks
Oh lord, You are correct Im sorry that was very very wrong. Sorry Hope he didnīt wright that down.

- January 9th 2010, 01:09 PMHenryt999Acctually I might be wrong again but....
You are correct the third side can not be 3 But has to be less.

If for example the angle is then it has area:

And Area is given by: That would give me a maximum area of 1??

If sides are: the last side would be ??

If this is the correct solution its not pretty, hope it was somewhat helpful.... - January 9th 2010, 10:19 PMGrandad
Hello everyoneYes, I think this is correct. I didn't have any more time to think about this yesterday (it's now 7:15 am UK time), but I had come to the same conclusion overnight. With as base, the maximum height possible is 1, where and the angle between these two sides is . So , and the area is sq unit.

Grandad