Find the value of y and
simplify completely.

y = 8

x = 8√5

z = 4√5

Step-by-step explanation:

Using the formula (which is a geometric mean):

a        y

=

x        a

Where a is the altitude (y), x is a projection (16), and y is the other projection (4):

y        4

=

16       y

Cross multiply:

y² = 16 (4)

y² = 64

√y² = √64

y = 8

To find x and z, use the Pythagorean Theorem:

16² + y² = x²

256 + 8² = x²

256 + 64 = x²

320 = x²

√320 = √x²

√64√5 = √x²

8√5 = x

x = 8√5

4² + y² = z²

16 + 64 = z²

80 = z²

√80 = √z²

√16√5 = √z²

4√5 = z

z = 4√5

Negative numbers would not make sense for the values of the variables especially when the equation represents a real world problem which mostly is the case. Having a negative value for a real world problem is not favorable because there is no such thing as negative time or negative height.