A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
[Work Included]
In ABC, centroid D is on median AM.
AD = x + 5 and DM = 2x – 1
Find AM.
 2 years ago
[Work Included] In ABC, centroid D is on median AM. AD = x + 5 and DM = 2x – 1 Find AM.

This Question is Closed

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1357236456605:dw

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1It looks more like an orthocenter, but for the sake of it, let's say it is a centroid.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1\[ x + 5 = 2x  1\]\[5 + x  2x = 2x  2x  1\]\[5  x = 1\]

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1Subtract five from both sides. \[x = 1  5\]\[x = 6\]

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1Now I can plug in the missing numbers. \[6 + 5 = 2(6)  1\]\[11 = 12  1\]\[= 11\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1I think you're incorrect in assuming that \(x+5\) must equal \(2x1\). 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.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1In that case, I'll tweak a few things here. \[x + 5 = 2(2x  1)\]\[x + 5 = 4x  2\] Subtracting 4 from both sides.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1\[5  3x = 2\]\[3x = 2  5\]\[3x = 7\]

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1\[x = \frac{ 7 }{ 3 }\]

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1That looks good to me. You can simplify that to \(\dfrac{7}{3}\) if you want.

enya.gold
 2 years ago
Best ResponseYou've already chosen the best response.1@KingGeorge The answer was really 11. Guess I should have trusted my gut, ha.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1Oops :( I guess that would be my fault.

KingGeorge
 2 years ago
Best ResponseYou've already chosen the best response.1However, I think we just forgot the last step in the problem. We found \(x=7/3\), but AM is equal to \((x+5)+(2x1)\). If we plug in our value for \(x\) into this, we get\[\frac{7}{3}+4+\frac{14}{3}=\frac{21}{3}+4=7+4=11\]
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.