Using the Geometric mean theorem and the Pythagorean theorem:
x = 3√3, and y = 6.
What is the Right Triangle Altitude Theorem/Geometric Mean Theorem?
The Geometric mean theorem or the right triangle altitude theorem states that the geometric mean of the the two segments equals he length of the altitude of a right triangle.
The geometric mean theorem is expressed by the equation, h = √(ab), where:
- a is the length of one segment
- b is the length of the other segment
- h is the length of the altitude of the right triangle.
Given the following:
h = x
a = 9
b = 3
x = √(9 × 3)
x = 3√3
Find y using the Pythagorean theorem
Based on the Pythagorean theorem, we would have the following:
y = √(x² + 3²)
y = √((3√3)² + 3²)
y = √(27 + 9)
y = √(36)
y = 6
Thus, in the simplest radical form, the value of x = 3√3, and y = 6.
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