The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments whose lengths are in the ratio of 1 : 2. The length of the altitude is 8 in.

Answer 1

I assume you had to find the segment lengths.

We did that.

We can find the lengths of the other sides, too, if you want.

Answer 2

What is the question to be answered?

If it find the lengths of the divided hypotenuse?

If so h*h = short length * long length

Since 2 * short length = long length,

h*h = s*2s = 2s²

h = s√2

So s = h/√2 = 8/√2 = 8√2/2 = 4√2.

And the long part = 2 * 4√2= 8√2.