# Triangle question (2)

1. Jul 4, 2009

### songoku

1. The problem statement, all variables and given/known data
P is a point on triangle ABC such that area PAB : area PBC : area PCA = 2 : 3 : 5
a. Find AQ : QC
b. Show that BP = 0.5 BQ

2. Relevant equations

3. The attempt at a solution
a. i found that AQ : QC = area QAB : area QBC, but i don't know how to continue ( the answer is 2 : 3)

b. sorry, i'm clueless...

thx

2. Jul 4, 2009

### HallsofIvy

Staff Emeritus
You mean in triangle ABC don't you?

Q? Where did Q come from? Do you mean P?

3. Jul 4, 2009

### songoku

oh sorry

yes P is a point inside the triangle and the straight line BP intersects the side AC at point Q.

thx

4. Jul 9, 2009

### harimakenji

i tried and got stuck at the same problem.....

anyone can help?

5. Jul 9, 2009

### snipez90

Hmm, I think the trick here is to keep using that fact that gave you AQ : QC = area QAB : area QBC, that is, for triangles with the same altitude but different bases, the ratio of their areas is just the ratio of their bases. The corresponding statement for same bases but different altitudes is also useful. I thought I had a solution but I made some pretty strong assumptions and have forgotten all about high school geometry, sorry I can't help further.

6. Jul 9, 2009

### kof9595995

Generally snipez90 is correct, but I can't explain it well without a diagram, I‘ll try to make a picture later.
Hint:Try constructing similar triangles

7. Jul 9, 2009

Here it is.

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8. Jul 9, 2009

### songoku

i think the term 'altitude' is the line that perpendicular to the opposite side.

Is BQ perpendicular to AC ?

thx

9. Jul 9, 2009

### kof9595995

No, BQ is not necessarily perpendicular to AC

10. Jul 9, 2009

### songoku

nice work

thx a lot all

11. Jul 9, 2009

### Leong

Coordinate geometry

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12. Jul 9, 2009

### Leong

Words have spreaded

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13. Jul 10, 2009

### songoku

wow, you use geometry coordinate again to solve triangle problem.

awesome !!!

thx a lot

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