Question

Solve for x! Please help!!

Answer 1

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

Explanation:

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

`(AB)/(AC)=(AD)/(AB)`

We have

AB = x

AC = 30

AD = 30 - 6 = 24

Susbtitute:

`(x)/(30)=(24)/(x)` cross multiply

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

`x^2=720\to x=√(720)`

`\begin{array}c720&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\\\\√(720)=√(2^2\cdot2^2\cdot3^2\cdot5)=√(2^2)\cdot√(2^2)\cdot√(3^2)\cdot\sqrt5=2\cdot2\cdot3\cdot\sqrt5=12\sqrt5`