## anonymous 3 years ago [Work Included] In ABC, centroid D is on median AM. AD = x + 5 and DM = 2x – 1 Find AM.

1. anonymous

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2. anonymous

It looks more like an orthocenter, but for the sake of it, let's say it is a centroid.

3. anonymous

$x + 5 = 2x - 1$$5 + x - 2x = 2x - 2x - 1$$5 - x = -1$

4. anonymous

Subtract five from both sides. $-x = -1 - 5$$-x = -6$

5. anonymous

$x = 6$

6. anonymous

Now I can plug in the missing numbers. $6 + 5 = 2(6) - 1$$11 = 12 - 1$$= 11$

7. KingGeorge

I think you're incorrect in assuming that $$x+5$$ must equal $$2x-1$$. The centroid of a triangle is located at a point 2/3 of the way along the median, and not 1/2 of the way along the median.

8. anonymous

In that case, I'll tweak a few things here. $x + 5 = 2(2x - 1)$$x + 5 = 4x - 2$ Subtracting 4 from both sides.

9. anonymous

$5 - 3x = -2$$-3x = -2 - 5$$-3x = -7$

10. anonymous

$x = \frac{ -7 }{ -3 }$

11. KingGeorge

That looks good to me. You can simplify that to $$\dfrac{7}{3}$$ if you want.

12. KingGeorge

You're welcome.

13. anonymous

@KingGeorge The answer was really 11. Guess I should have trusted my gut, ha.

14. KingGeorge

Oops :( I guess that would be my fault.

15. KingGeorge

However, I think we just forgot the last step in the problem. We found $$x=7/3$$, but AM is equal to $$(x+5)+(2x-1)$$. If we plug in our value for $$x$$ into this, we get$\frac{7}{3}+4+\frac{14}{3}=\frac{21}{3}+4=7+4=11$