[tex]x=9 \sqrt{3}[/tex]
Step-by-step explanation:
The image is attached below.
Given AB = 9
BC = x
AC = y = 18
Note that the given triangle is a right angled triangle.
We know that Pythagoras theorem states that in a right angle hypotenuse is equal to the sum of the squares of other two sides.
Using Pythagoras thereom,
[tex]A C^{2}=A B^{2}+B C^{2}[/tex]
[tex]18^{2}=9^{2}+x^{2}[/tex]
[tex]324=81+x^{2}[/tex]
[tex]x^{2}=324-81[/tex]
[tex]$x^{2}=243$[/tex]
Taking square root on both sides,
[tex]x=\sqrt{9 \times 9 \times 3}[/tex]
[tex]$x=9 \sqrt{3}$[/tex]
Hence, the value of x is [tex]9 \sqrt{3}[/tex].
