the complete question in the attached figure
we know that
The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse
h²=x*y
where
h is the length of the altitude to the hypotenuse
h=12
x and y are the two segments of the hypotenuse
so
12²=x*y----------> 144=x*y
the lengths of the two segments of the hypotenuse could be
x=6
y=24
x*y=144
the answer is
6 and 24