To find the length of the line \( x \) using the geometric mean, we can apply the geometric mean theorem, which states that the length of the altitude from the vertex opposite the hypotenuse to the hypotenuse is the geometric mean of the two segments it divides the hypotenuse into.
Given that the hypotenuse is divided into segments of 5 and 12, we denote these segments as \( a = 5 \) and \( b = 12 \). According to the theorem, the length of \( x \) is given by:
\[ x = \sqrt{a \cdot b} \]
Substituting \( a \) and \( b \):
\[ x = \sqrt{5 \cdot 12} = \sqrt{60} \]
Calculating this:
\[ x = \sqrt{60} \approx 7.75 \]
Thus, the value of \( x \) is approximately \( 7.75 \).
The correct response is:
7.75
1 answer