As per the geometric mean theorem of a triangle, the value of 'a' is 2√(70).
"The geometric mean theorem describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of the two segments equals the altitude."
Given, AC = b, CA = a, CD = h.
The hypotenuse has two sections AD and DB.
AD = 6, DB = 14
Therefore, in triangle ABC:
(CD)² = AD × DB
⇒ CD² = (AD × DB)
⇒ CD² = (6 × 14)
⇒ CD² = 84
Now, ΔBCD is also a right angle triangle.
Therefore, (BC)² = (CD)² + (DB)²
⇒ a² =  84 + (14)²
⇒ a² = 280
⇒ a = 2√(70)
Learn more about the geometric mean theorem of a triangle here: https://brainly.com/question/24095553
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