Question

If the ratio of the legs of a right triangle is 1 : 2, then the ratio of the corresponding segments of the
hypotenuse made by a perpendicular upon it from the vertex is

Answer 1

Let the altitude h from the right angle divide the hypotenuse into two sections x and y, with x<y.

By similar triangles, we see that

h/x = 2/1
h/y = 1/2

x/y = (h/y)/(h/x) = (1/2)/(2/1) = 1/4