Question

use the geometric mean (leg) theorem. what is the value of a?
7√2
2√70
20√5
70√5

Explanation:

Step1: Apply the geometric mean (leg) theorem

The geometric mean (leg) theorem states that in a right - triangle, the length of a leg is the geometric mean of the length of the hypotenuse and the length of the projection of that leg on the hypotenuse. For leg \(a\) in \(\triangle ABC\) with right - angle at \(C\) and altitude \(CD\), \(a^{2}=BD\times(BD + AD)\).
Given \(BD = 14\) and \(AD=6\), then \(a^{2}=14\times(14 + 6)\).

Step2: Calculate the value of \(a^{2}\)

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Step3: Find the value of \(a\)

Take the square root of \(a^{2}\), \(a=\sqrt{280}\). Simplify \(\sqrt{280}=\sqrt{4\times70}=2\sqrt{70}\).

Answer:

\(2\sqrt{70}\)