Question

NEED HELP
what is X in the diagram ​

Answer 1

`x=6√(3)`

Explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ABC

Applying the Pythagoras Theorem

Find out the length side AB

`AC^2=AB^2+BC^2`

`AB^2=AC^2-BC^2`

substitute the given values

`AB^2=12^2-x^2`

`AB^2=144-x^2`

step 2

In the right triangle ABD

Applying the Pythagoras Theorem

Find out the length side BD

`AB^2=AD^2+BD^2`

`BD^2=AB^2-AD^2`

substitute the given values

`BD^2=144-x^2-3^2`

`BD^2=144-x^2-9`

`BD^2=135-x^2` -----> equation A

step 3

In the right triangle BCD

Applying the Pythagoras Theorem

Find out the length side BD

`BC^2=DC^2+BD^2`

`BD^2=BC^2-DC^2`

substitute the given values

`BD^2=x^2-9^2`

`BD^2=x^2-81` -----> equation B

step 4

equate equation A and equation B

`BD^2=135-x^2` -----> equation A

`BD^2=x^2-81` -----> equation B

`x^2-81=135-x^2`

`x^2+x^2=135+81`

`2x^2=216`

`x^2=108`

`x=√(108)`

Simplify

`x=6√(3)\ units`