Question

given right triangle abc with altitude bd drawn to hypotenuse ac. if ac = 24 and dc = 6, what is the length of bc?

Explanation:

Step1: Use geometric mean theorem

In a right - triangle, the altitude to the hypotenuse is the geometric mean between the segments of the hypotenuse. Also, \(BC^{2}=CD\times AC\).

Step2: Substitute the values

Given \(CD = 6\) and \(AC=24\). Substitute these values into the formula \(BC^{2}=CD\times AC\). So \(BC^{2}=6\times24\).

Step3: Calculate \(BC^{2}\)

\(6\times24 = 144\). Then, to find \(BC\), take the square root of \(144\). Since \(BC>0\), \(BC=\sqrt{144}\).

Answer:

\(12\)