web2.0calc
 
+0  
 

​Geometry- triangle medians and altitudes.

+1
692
4
avatar+781 

What I've done so far is extend a lie from point Q to R to form an isoceles triangle. Then using the side lengths given in the problem, I found that line QR was \sqrt{193}. I don't really know what to do from there. Should I form a ratio for triangle QNR and ORN since they appear to be similar?

 Jul 29, 2020

4+0 Answers

 #1
avatar
0

QN = 12                PR = 14       PN = 7

 

F is a foot of the altitude from M to PN

 

Find angle QPN using QN and PN

 

Find QP and MP using the Pythagorean theorem

 

Find MF and PF using angle QPN and MP

 

Find angle MRF using MF and FR

 

And finally, find  OR = 5*sqrt(2).

 Jul 29, 2020
 #4
avatar
0

"And finally, find  OR = 5*sqrt(2)"         5*sqrt(2) = 7.07106781   INCORRECT !!!

 

The correct answer is:        OR = 7 / cos(29.7448813º) = sqrt(65)smiley 

Guest Jul 29, 2020
edited by Guest  Jul 29, 2020
 #2
avatar+1490 
0

There's a shortcut:::

 

Important:   The ratio of  QO  to  NO is  2 : 1        ( The Median Theorem )

 

NR = 1/2 * 14 = 7            ( QN ⊥ PR )

 

NO = 1/3 * 12 = 4

 

OR = sqrt (72 + 42) = √65 

 Jul 29, 2020
edited by Dragan  Jul 29, 2020
 #3
avatar+781 
+2

Ohh so I just needed to apply this theorem?

gwenspooner85  Jul 29, 2020

3 Online Users

Top Users

avatar+37146 ElectricPavlov
avatar+33661 Alan moderator
avatar+14995 asinus moderator
avatar+9673 MaxWong
avatar+2489 GingerAle
avatar+1894 NotThatSmart
avatar+1839 ABJeIIy
avatar+1768 bader
avatar+1525 parmen
avatar+1439 kittykat
avatar+1427 blackpanther

Sticky Topics