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