Question

in the figure below, b is between a and c, and c is between b and d. if ac = 11, bd = 13, and bc = 6, find ad.

Explanation:

Step1: Find length of CD

Since \(BD = 13\) and \(BC=6\), and \(BD=BC + CD\), then \(CD=BD - BC\).
\(CD = 13 - 6=7\)

Step2: Find length of AC

Given \(AC = 11\) and \(BC = 6\), and \(AC=AB + BC\), we don't need to find \(AB\) for our final answer. We know that \(AD=AC + CD\).

Step3: Calculate AD

Substitute the values of \(AC = 11\) and \(CD = 7\) into the formula \(AD=AC + CD\).
\(AD=11 + 7 = 18\)

Answer:

18