If the altitude drawn to the hypotenuse of a right triangle has length 10, the lengths of the segments of the hypotenuse may be: a) 2 and 5 b) 50 and 50 c) 5 and 20 d) 3 and 7

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