Question

The length of the altitude drawn to the hypotenuse of a right triangle is 8. What could be the possible lengths of the segments of the hypotenuse?
4 and 4
4 and 8
4 and 16
4 and 64

Answer 1

You need the theorem: If an altitude is drawn to the hypotenuse of a right triangle, the altitude is the geometric mean between the lengths of the segments of the hypotenuse.

That means that 8 = √(x*y) where x and y are the segments of the hypotenuse.
Look at the answer options for two numbers the square root of whose product is 8, i.e., the numbers multiply to 64.

4 and 16 ---> Answer