What is the measure of n?

Given:

A figure of a right triangle whose altitude divides the opposite in two segments of 8 and 4 units.

The measure of the altitude is n.

To find:

The value of n.

Solution:

According to the altitude on hypotenuse theorem, the altitude on the hypotenuse of a right triangle is geometric mean of two segments of the hypotenuse.

Let the altitude h divides the hypotenuse in two parts with measure a and b, then

[tex]\dfrac{h}{a}=\dfrac{b}{a}[/tex]

[tex]h^2=ab[/tex]

[tex]h=\sqrt{ab}[/tex]             [Because side length cannot be negative]

In the given figure, the altitude is n and it divides the hypotenuse in two segments of 8 units and 4 units.

Using altitude on hypotenuse theorem, we get

[tex]\dfrac{n}{8}=\dfrac{4}{n}[/tex]

[tex]n^2=4\times 8[/tex]

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

[tex]n=\sqrt{32}[/tex]

Therefore, the measure of altitude is [tex]n=\sqrt{32}[/tex] units.

finding the slope to points ​

Geraldo has 3 fewer marbles than Yan Together, they have 21 marbles which equation
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Plz help this is due today NO LINKS OR GROSS PICTURES OR I Will REPORT And please show work

Can someone help me really please

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