Question

Solve for x! Please help!!

Answer 1

Answer:

$\large\boxed{x=12\sqrt5}$

Step-by-step explanation:

ΔABC and ΔABD are similar (AA). Therefore the sides are in proportion:

$\dfrac{AB}{AC}=\dfrac{AD}{AB}$

We have

AB = x

AC = 30

AD = 30 - 6 = 24

Susbtitute:

$\dfrac{x}{30}=\dfrac{24}{x}$           cross multiply

$x^2=(30)(24)$

$x^2=720\to x=\sqrt{720}$

$\begin{array}{c|c}720&2\\360&2\\180&2\\90&2\\45&3\\15&3\\5&5\\1\end{array}\\\\720=2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot5=2^2\cdot2^2\cdot3^2\cdot5\\\\\sqrt{720}=\sqrt{2^2\cdot2^2\cdot3^2\cdot5}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{3^2}\cdot\sqrt5=2\cdot2\cdot3\cdot\sqrt5=12\sqrt5$