We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
-1
201
2
avatar+526 

The medians of a particular right triangle drawn from the vertices of the acute angles are 5 units and √ 40 units. What is the length of the median drawn from the right angle? Express your answer as a decimal to the nearest tenth.

 Dec 9, 2018
 #1
avatar+101760 
+2

Call the lengths of the two legs x and y

 

We have this system of equations

 

x^2 + [(1/2)y]^2 = 25   ⇒  x^2 + (1/4)y^2 = 25    (1)

 

[(1/2)x]^2 + y^2 = 40    ⇒  (1/4)x^2 + y^2 = 40   (2)

 

Multiply equation (1)  through by -4 and we have this system

 

-4x^2   - y^2 =  -100

(1/4)x^2 + y^2 = 40       add these

 

-(15/4)x^2 = - 60

x^2 = 16

x = 4

 

And using (2) to find y, we have

 

(1/4)(4)^2 + y^2 = 40

4 + y^2 = 40

y^2 = 36

y = 6

 

So....the hypotenuse length is   sqrt (4^2 + 6^2 )  =  sqrt (52) = 2sqrt  (13)

 

And in a right triangle, the median drawn from the right angle is 1/2 the hypotenuse length = 

 

sqrt (13)

 

 

cool cool cool

 Dec 9, 2018
 #2
avatar+526 
+1

Here's the diagram I think you're talking about.

dgfgrafgdfge111  Dec 9, 2018

10 Online Users

avatar