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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+98107 
+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+417 
+1

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

dgfgrafgdfge111  Dec 9, 2018

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