Answer:
[tex]x = 2\sqrt{11}[/tex]
Step-by-step explanation:
According to the pythagorean theorem,
[tex]a^2 + b^2 = c^2[/tex]
where a and b are the legs of a right triangle, and c is the hypotenuse.
Starting in the left triangle to find the hypotenuse,
[tex]6^2 + 8^2 = c^2\\36 + 64 = c^2\\100 = c^2\\c = 10[/tex]
We can then use the hypotenuse to find the value of x using the pythaogrean theorem in the right triangle.
[tex]10^2 + x^2 = 12^2\\100 + x^2 = 144\\x^2 = 44\\x = \sqrt{44} = 2\sqrt{11}[/tex]
