Question

applying the geometric mean (leg) theorem
what is the value of q?
64√5
20√5
2√14
4√5

Explanation:

Step1: Apply the geometric mean (leg) theorem

The geometric mean (leg) theorem states that in a right - triangle, the leg of the triangle is the geometric mean between the hypotenuse and the segment of the hypotenuse adjacent to that leg. For right - triangle \(QRS\) with right - angle at \(S\) and altitude \(ST\), we have the formula \(q=\sqrt{4\times(4 + 10)}\).

Step2: Simplify the expression

First, calculate the value inside the square root: \(4\times(4 + 10)=4\times14 = 56\). Then, \(\sqrt{56}=\sqrt{4\times14}=2\sqrt{14}\).

Answer:

\(2\sqrt{14}\)