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

1. By the Altitud Rule, you have:

 Segment1/Altitud=Segment 2/Altitud

 2. The ratio is 1:2, then:

 Segment1=2x

 Segment2=1x
 Segment2=x

 Altitud=8

 3. When you apply the Altitud Rule, you obtain:

 Segment1/Altitud=Segment 2/Altitud
 2x/8=8/x

 4. When you clear the "x", you have:

 (2x)(x)=(8)(8)
 2x²=64
 x²=64/2
 x²=32
 x=√32
 x=4√2

 5. Then:

 2x=2(4√2)=8√2

 6. Therefore, the lenght of the hypotenuse is:

 h=4√2+8√2
 h=12√2
 h=16.97