+0  
 
0
1123
2
avatar+1760 

 

A median of a triangle is a line segment from a vertex of a triangle to the midpoint of the opposite side of the triangle. The medians to the legs of a certain right triangle have lengths 13 and 19. What is the length of the hypotenuse of the triangle?

Mellie  Nov 14, 2015

Best Answer 

 #1
avatar+26329 
+15

My interpretation is as follows:

 

medians

Alan  Nov 15, 2015
Sort: 

2+0 Answers

 #1
avatar+26329 
+15
Best Answer

My interpretation is as follows:

 

medians

Alan  Nov 15, 2015
 #2
avatar+78754 
+10

Let L1 be the length of one of the legs and L2 be the lentgh of the other.......and by the Pythagorean Theorem ,we have that

 

[L1]^2 + [(1/2)L2] ^2 = 19^2     and

 

[L2]^2 + [(1/2)L1]^2  = 13^2   simplify

 

 

L1^2 + (1/4)L2^2  = 361     (1)

L2^2 + (1/4)L1^2  = 169     (2)

 

Rearranging (1),we  have

 

L1^2  = 361  - (1/4)L2^2   (3)    and subbing this into (2),we have

 

L2^2 +(1/4)[ 361 - (1/4)L2^2 ] = 169     multiply through by 16

 

16L2^2 + 4*361 - L2^2  = 2704

 

15L2^2  = 2704 - 4*361 

 

15L2^2 = 1260     divide by 15

 

L2^2 = 84   →  L2 = 2sqrt(21)

 

And using (3), we have

 

L1^2 = 361 - (1/4)L2^2

 

L1^2 = 361 - (1/4)84

 

L1^2  = 361 - 21

 

L1^2  = 340  →  L1 = 2sqrt(85)

 

So....the hypotenuse =  sqrt (84 + 340) =  sqrt (424) = 2sqrt (106)

 

 

 

cool cool cool

CPhill  Nov 15, 2015

9 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details