Question

Find the value of the variable.​

Answer 1

Answer:

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

Step-by-step explanation:

Look at the picture.

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

$\dfrac{AB}{BC}=\dfrac{BD}{AB}$

We have

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

Substitute:

$\dfrac{x}{9}=\dfrac{5}{x}$             cross multiply

$x^2=(9)(5)\to x=\sqrt{(9)(5)}\\\\x=\sqrt9\cdot\sqrt5\\\\x=3\sqrt5$