Math Is Fun Forum

Ral

Guest

Need some help finding the side of a triangle...

All right, so I am in Geometry and I just learned centroid theorem and how to find the orthocenter.

So, Triangle GHJ is drawn with 3 medians labeled GL, KJ and HM, and they intersect at P. Line GL has a right angle which I think means that's an altitude.

So I'm given GP=8, LJ=5 and HK=6.5. I'm also given that GK=KH, GM=MJ, and HL=LJ

I found out that:

1.GL=12, since GP=8 and the centroid theorem says that the centroid of a triangle is 2/3 of the distance from each vertex to the midpoint of the opposite side and  LP is the other 1/3 so it has to be 4

2.PL is 4, for the reasons mentioned above

3.HL=5, since LJ=5 and since HL=LJ, it has to be 5

4.GJ=...? This is where I get stuck. I know GM=MJ, but neither side is given.

5.perimeter of triangle GHJ: I can't answer this because I don't have the answer for the above

6.Area of triangle GHJ: This one should be easy, ½baseXheight. the height is 12 (since I was given that little right angle signaling GL is an altitude and altitude=height, the height is 12) now for the base... Well, that killed my steam. I don't know that. Because the base is GJ and I can't find GJ...

So what am I missing here? This is really killing me here, since I'm trying to rack my brains on how to find it out and I'm sure it's so simple, but it completely eludes me. Thank you for listening to my triangle problems and here's to hoping someone knows what I'm not getting.

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: Need some help finding the side of a triangle...

Hi Ral,
     Try this...
    You can easily find

and

.
Once you know those two angles (actually you only need

) you can find

by the law of sines.
You will then be able to determine

.
OK.  So on

, you now know two sides and the angle inbetween so the other side can be found by the law of cosines.

Last edited by Fruityloop (2009-10-22 16:03:54)