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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

Respuesta :

carlosego
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 
MrRoyal

The hypotenuse is 17.1 inches long

Given that the scale ratio is 1 : 2.

This means that:

Segment 1 : Segment 2 = 1 : 2

This gives

Segment 1 : Segment 2 = x : 2x

By comparison,

Segment 1 = x

Segment = 2x

Using the Altitude rule, x is then calculated as:

[tex]\frac{Segment\ 2}{8} = \frac{8}{Segment\ 1}[/tex]

Substitute known values

[tex]\frac{2x}{8} = \frac{8}{x}[/tex]

Cross multiply

[tex]2x^2 = 64[/tex]

Divide through by 2

[tex]x^2 = 32[/tex]

Take the square root of both sides

[tex]x = 5.7[/tex]

The length of the hypotenuse (h) is then calculated as:

[tex]h =x + 2x[/tex]

[tex]h =3x[/tex]

[tex]h =3 * 5.7[/tex]

[tex]h =17.1[/tex]

Hence, the hypotenuse is 17.1 inches long

Read more about right triangles at:

https://brainly.com/question/2437195

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