Answer:
[tex]\large\boxed{x=12\sqrt5}[/tex]
Step-by-step explanation:
ΔABC and ΔABD are similar (AA). Therefore the sides are in proportion:
[tex]\dfrac{AB}{AC}=\dfrac{AD}{AB}[/tex]
We have
AB = x
AC = 30
AD = 30 - 6 = 24
Susbtitute:
[tex]\dfrac{x}{30}=\dfrac{24}{x}[/tex] cross multiply
[tex]x^2=(30)(24)[/tex]
[tex]x^2=720\to x=\sqrt{720}[/tex]
[tex]\begin{array}{c|c}720&2\\360&2\\180&2\\90&2\\45&3\\15&3\\5&5\\1\end{array}\\\\720=2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5=2^2\cdot2^2\cdot3^2\cdot5\\\\\sqrt{720}=\sqrt{2^2\cdot2^2\cdot3^2\cdot5}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}\cdot\sqrt5=2\cdot2\cdot3\cdot\sqrt5=12\sqrt5[/tex]
