+936 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.
+128408 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)
