Respuesta :

frika

Answer:

[tex]x=6\sqrt{5}\\ \\y=3\sqrt{5}\\ \\z=6[/tex]

Step-by-step explanation:

The height of the right triangle drawn to the hypotenuse is geometric mean of two segments of hypotenuse, so

[tex]z^2=12\cdot 3\\ \\z^2=36\\ \\z=6[/tex]

By the Pythagorean theorem,

[tex]x^2=12^2+z^2\\ \\x^2=144+6^2\\ \\x^2=144+36\\ \\x^2=180\\ \\x=6\sqrt{5}[/tex]

and

[tex]y^2=z^2+3^2\\ \\y^2=6^2+9\\ \\y^2=36+9\\ \\y^2=45\\ \\y=3\sqrt{5}[/tex]

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