+1533 In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?
+129850 A
N
C M B
AC^2 + [ (BC)/2 ] ^2 = 1
(AC/2)^2 + BC^2 = 1
AC^2 + BC^2/4 = 1
AC^2/4 + BC^2 = 1
4AC^2 + BC^2 = 4
AC^2/4 + BC^2 = 1 subtract these
(15/4)AC^2 = 3
AC^2 = 12/15 = 4/5
(12/15)/2 + BC^2 = 1
(2/5) + BC^2 =1
BC^2 = 4/5
AB = sqrt [ AC^2 + BC^2 ] = sqrt [ 4/5 + 4/5 ] = sqrt [ 8/5] = (2/5)sqrt (10)
