Question

Can anybody help with this answer?? Use the geometric mean or Pythagorean theorem to solve for z

Answer 1

The answer to your question is z =
`√(24)`

Explanation:

Process

I'll solve this problem using proportions, I hope it helps you

We consider the adjacent side of both triangle

Adjacent side small triangle = x Adjacent side big triangle = 10

Proportion of these sides =
`(x)/(10)`

Now, consider the opposite side of both triangles

Opposite side fo small triangle = 2 Opposite side big triangle = x

Proportion =
`(2)/(x)`

Now, equal both proportions and solve for x

`(x)/(10) = (2)/(x)`

x² = 20

x =
`√(20)`

x = 2
`√(5)`

Using Geometric mean

x =
`√(2x10) = √(20)`

Using the Pythagorean theorem to find z

z² = (√20)² + 2²

z² = 20 + 4

z² = 24

z =
`√(24)`