Question

Find the value of x.

Answer 1

`\huge\boxed{y=√(55)}`

Explanation:

ΔADC and ΔDBC are similar (AAA)

Therefore the cooresponging sides are in proportion:

`(AC)/(CD)=(CD)/(BC)`

Substitute:

`AC=6+5=11\\BC=5\\CD=y`

`(11)/(y)=(y)/(5)` cross multiply

`(11)(5)=(y)(y)\\\\55=y^2\to y=√(55)`