Question

Find the value of x.

Answer 1

Answer:

$\large\boxed{2\sqrt7}$

Step-by-step explanation:

Look at the picture.

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

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

We have

$AC=x,\ AD=2,\ AB=2+12=14$

Substitute:

$\dfrac{x}{2}=\dfrac{14}{x}$           cross multiply

$x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7$