Answer:
[tex]x=3\sqrt{2}[/tex]
Step-by-step explanation:
In a right triangle, the "hypotenuse" is the side opposite of the 90 degree angle. That side is "a"
Using pythagorean theorem, we can write:
Leg^2 + Leg^2 = Hypotenuse^2
Note: legs are the other 2 sides, x and x respectively
Now we can write:
[tex]x^2 + x^2 = a^2[/tex]
a is 6 meters, so replacing a with 6 and solving we get:
[tex]x^2 + x^2 = a^2\\2x^2=6^2\\2x^2=36\\x^2=18\\x=\sqrt{18}[/tex]
To simplify the surd, we can use the property shown below:
[tex]\sqrt{x*y}=\sqrt{x} \sqrt{y}[/tex]
Also
[tex]\sqrt{x} \sqrt{x} =x[/tex]
Now simplifying:
[tex]x=\sqrt{18} \\x=\sqrt{9*2}\\ x=\sqrt{9} \sqrt{2} \\x=3\sqrt{2}[/tex]
