Question

20 fill in the blank 1 point
in the diagram below, bc is an altitude of triangle abd. to the nearest whole unit, what is the length of cd?
choose your answer_
choose your answer_
18
23
20
15
pr

Explanation:

Step1: Apply the geometric mean theorem (altitude - on - hypotenuse theorem)

In a right - triangle \(ABD\) with altitude \(BC\) to the hypotenuse \(AD\), we have the formula \(BC^{2}=CD\times AC\). Let \(CD = x\). We know that \(BC = 32\) and \(AC=44\). So, \(32^{2}=x\times44\).

Step2: Solve for \(x\)

From \(32^{2}=x\times44\), we get \(x=\frac{32^{2}}{44}\). Calculate \(32^{2}=1024\). Then \(x = \frac{1024}{44}\approx23.27\).

Answer:

\(23\)