Math Is Fun Forum

I have seen this type of question but in it AD was the median if it is the median then
in triangle ABC
(AB)²+(AC)²=(BC)²=81
in triangle ACD
angle ADC is 90 degree as AD is median
x²+36=(AC)²   x²=(AC)²-36
and similarly triangle ABD
x²+9=(AB)²    x²=(AB)²-9
(AB)²=(AC)²-36+9=(AC)²-27
(AB)²-(AC)²=-27
(AB)²+(AC)²=81
adding equations
2(AB)²=81-27
AB=3√3
x=3√2