we know that
the length of this altitude is the geometric mean between the lengths of these two segments
see the attached figure to better understand the problem
if the two segments are x and y then
so
10²=x*y---------> 100=x*y
case A) 2 and 5
x=2
y=5
5*2 is not 100
B) 50 and 50
x=50
y=50
50*50 is not 100
C) 5 and 20
x=5
y=20
5*20 is 100----------> 5 and 20 maybe the hypotenuse
D) 3 and 7
x=3
y=7
3*7 is not 100
the answer is the option
C) 5 and 20
