Find x, y and z to the nearest hundredth.

see explanation

Step-by-step explanation:

This is an example of the Altitude - on - Hypotenuse theorem.

The altitude that is perpendicular to the hypotenuse of a right triangle.

The two triangles formed are similar to the given triangle and to each other.

x² = (smaller part) × (larger part) of main hypotenuse

x² = 6 + 19 = 114 ( square root both sides )

x ≈ 10.68 ( nearest hundredth )

y² = ( smaller part) × (whole part) of main hypotenuse

y² = 6 × 25 = 150 ( square root both sides )

y ≈ 12.25 ( nearest hundredth )

z² = ( larger part) × (whole part) of main diagonal

z² = 19 × 25 = 475 ( square root both sides )

z ≈ 21.79 ( nearest hundredth )