Question

NEED HELP what is X in the diagram ​

Answer 1

Answer:

$x=6\sqrt{3}$

Step-by-step 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

$x^2-81=135-x^2$

$x^2+x^2=135+81$

$2x^2=216$

$x^2=108$

$x=\sqrt{108}$

Simplify

$x=6\sqrt{3}\ units$