Question

Find the value of x.

Answer 1

`\large\boxed{2\sqrt7}`

Explanation:

Look at the picture.

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

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

We have

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

Substitute:

`(x)/(2)=(14)/(x)` cross multiply

`x^2=(2)(14)\\\\x^2=28\to x=√(28)\\\\x=√(4\cdot7)\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7`