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what is the measure of z? 3 27 y x z

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$$3\sqrt{10}$$

Step-by-step explanation:

By the geometric mean theorem,

$$\frac{y}{3}=\frac{27}{y}\\y^{2}=81\\y=9$$

So, by the Pythagorean theorem,

$$3^{2}+9^{2}=z^{2}\\90=z^{2}\\z=\boxed{3\sqrt{10}}$$
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