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.

dgfgrafgdfge111 Dec 9, 2018

#1**+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)

CPhill Dec 9, 2018