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Medians DP and EQ of triangle DEF are perpendicular. If DP = 18 and EQ = 28, then what is DF?

 Apr 21, 2022
 #1
avatar+124596 
+1

    D

 

                         

                                 Q

              

                M

 

 

E                       P                                 F

 

 

Let M  be the intersection point of the two medians

 

By the property  of medians    DM  = (2/3)18 =  12     MQ =  (1/3) 28  =  28 / 3

 

So....since  DP and EQ  are perpendicular.....then     DQ =  sqrt [ 12^2  + (28/3)^2 ]  = 

 

sqrt [ 144  + 784/9 ] =   sqrt    [ 1296 + 784 ]  / 3  =  sqrt [ 2080 ] / 3  =     4sqrt (130) / 3

 

And DF =   2 DQ  =      2 * 4sqrt (130) / 3    =   (8/3)sqrt (130)

 

cool cool cool

 Apr 21, 2022
edited by CPhill  Apr 21, 2022
 #2
avatar+115 
-4

something ver similar to what you got look at this https://web2.0calc.com/questions/please-help-with-these-geometry-questions

▄︻デ✞✞🅚🅐🅚🅐🅢🅗🅘✞✞══━一

 Apr 21, 2022

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