Question

Solve for the missing variables. (Geometry)

Answer 1

Hi!

Let's start by finding the Geometric mean (see image below for additional info):

`\cfrac{7}{z} =\cfrac{z}{(9+7)}`

Therefore, using the Cross Products Property of Proportions, we can set up this equation:

`z^2=112`

`z=√(112)`

Simplified:

`z=4√(7)`

Now, we can use the Geometric Mean to solve for x as well:

`\cfrac{9}{x} =\cfrac{x}{7}`

Therefore:

`63=x^2`

Solving, we get:

`x=√(63)`

Simplified:

`x=3√(7)`

Now, we can use it once again:

`\cfrac{y}{16} =\cfrac{9}{y}`

Therefore:

`144=y^2`

`y=12`