Hi!
Let's start by finding the Geometric mean (see image below for additional info):
[tex]\cfrac{7}{z} =\cfrac{z}{(9+7)}[/tex]
Therefore, using the Cross Products Property of Proportions, we can set up this equation:
[tex]z^2=112[/tex]
[tex]z=\sqrt{112}[/tex]
Simplified:
[tex]z=4\sqrt{7}[/tex]
Now, we can use the Geometric Mean to solve for x as well:
[tex]\cfrac{9}{x} =\cfrac{x}{7}[/tex]
Therefore:
[tex]63=x^2[/tex]
Solving, we get:
[tex]x=\sqrt{63}[/tex]
Simplified:
[tex]x=3\sqrt{7}[/tex]
Now, we can use it once again:
[tex]\cfrac{y}{16} =\cfrac{9}{y}[/tex]
Therefore:
[tex]144=y^2[/tex]
[tex]y=12[/tex]
