Answer:
[tex]AD \approx 15.6\,cm[/tex]
Step-by-step explanation:
The value of AD is found by using the Pyhagorean Theorem:
[tex]AD = \sqrt{CD^{2}+AC^{2}}[/tex]
[tex]AD = \sqrt{CD^{2}+4\cdot AB^{2}}[/tex]
[tex]AD^{2} - 4\cdot AB^{2} = CD^{2}[/tex]
Besides, BD is measured in terms of the Pythagorean Theorem:
[tex]BD = \sqrt{CD^{2}+AB^{2}}[/tex]
[tex]BD^{2} - AB^{2} = CD^{2}[/tex]
By Algebra:
[tex]AD^{2}-4\cdot AB^{2} = BD^{2} - AB^{2}[/tex]
[tex]AD^{2} = BD^{2}+3\cdot AB^{2}[/tex]
[tex]AD = \sqrt{BD^{2}+3\cdot AB^{2}}[/tex]
[tex]AD = \sqrt{(13\,cm)^{2}+3\cdot (5\,cm)^{2}}[/tex]
[tex]AD \approx 15.6\,cm[/tex]
