Question

in the diagram below, $overline{bc}$ is an altitude of $\triangle abd$. to the nearest whole unit, what is the length of $overline{cd}$? a. 52 b. 44 c. 56 d. 58

Explanation:

Step1: Apply geometric - mean theorem

In a right - triangle formed by altitude \(BC\) in \(\triangle ABD\), we have \(BC^{2}=AC\times CD\). Given \(BC = 30\) and \(AC=16\). Let \(CD=x\). Then \(30^{2}=16x\).

Step2: Solve for \(x\)

We have the equation \(900 = 16x\). So, \(x=\frac{900}{16}=56.25\).

Answer:

C. 56