Geometry help

[java]

put on your math hats

sketch a triangle ABC and locate a point on BC such that AP bisects the triangle. If the perimeter of the triangle is 44. BP=6 and PC=10
find AB and AC

anyone???

 

[mrsv98]

ok, I think I have this

draw a right triangle A is the bottom left corner, B is the top and C is bottom right. Draw "P" from the corner where A is bisecting BC. BP is 6 and PC is 10 making BC 16, leaving 28. IF BA and AC are equal, they are both then 14.

Does that make ANY sense? Jesus was a baby the last time I did this but I used to be pretty good in Geometry. I will try to draw a pic and post it.

 

[java]

Thanks for trying but it's not a RIGHT angle. unfortunatly.

We know the answer is 10.5 and 17.5 but don't know how to get there.

 

[Disneycrazymom]

Does it show any of the angles being equal? Is there any other information from another problem but related to this one?

 

[java]

The only angle that you would know is that the one bisecting point A on either side of the now created triangles would be equal.
oh man my head hurts. And I was good in math. Having children dumbed me down I think.

 

[Master Mason]

Does it show any of the angles being equal? Is there any other information from another problem but related to this one?

Take a look at this website http://www.clarku.edu/~djoyce/trig/area.html It tells you how to figure the area of a triangle using the lenght of the sides. You know that the areas of the two new triangles are the same and 2 of each traingles legs, so you should be able to solve for the 3rd with this.

 

[DisneyBamaFan]

Figured it out - getting old.

Use the angle bisector theorem - it relates the length of the side opposite one angle of a triangle to the lengths of the other two sides of the triangle when equally bisected.

Consider a triangle ABC. Let the angle bisector of angle A intersect side BC at a point P. The angle bisector theorem states that the ratio of the length of the line segment BP to the length of segment PC is equal to the ratio of the length of side AB to the length of side AC

6/10 = .6 so the ratio of AB to AC would also be .6. The perimeter is 44, less the side 16 in length = 28.

Find 2 numbers that add up to 28, that also have a ratio of 6/10.
A + .6 A = 28 or
1.6A = 28 or
28/1.6 = A
A = 17.5

 

[DisneyBamaFan]

My 11 year old just told me to finish the problem:

So, if one side is 16 (10 + 6), and the other is 17.5, and the perimeter is 44, then the last side is 10.5

B + 16 + 17.5 = 44
B + 33.5 = 44
B = 44 - 33.5
B = 10.5

 

[damo]

AC/10 = AB/6

so AC = 5/3 AB

AB + BC + AC = 44
AB + 16 + 5/3 AB = 44
8/3 AB = 44-16
8/3 AB = 28
AB = 10.5

 

[Disneycrazymom]

Nice work Damo!

Here is a tutorial site: http://www.mathwarehouse.com/geometry/similar/triangles/angle-bisector-theorem.php

 

[java]

THANK YOU ALL SO MUCH!!!

I knew we had math geniuses on this board!
Damo's way is the way I was trying to figure it out to begin with but I couldn't get the 8/3 duh!
Thank you all again! The Dis ROCKS.