Question

Find the value of the variable.​

Answer 1

`\large\boxed{x=3\sqrt5}`

Explanation:

Look at the picture.

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

`(AB)/(BC)=(BD)/(AB)`

We have

`AB=x,\ BC=5+4=9,\ BD=5`

Substitute:

`(x)/(9)=(5)/(x)` cross multiply

`x^2=(9)(5)\to x=√((9)(5))\\\\x=\sqrt9\cdot\sqrt5\\\\x=3\sqrt5`