Answer:
9[tex]\sqrt{2}[/tex] inches
or
12.728 inches
Step-by-step explanation:
Use Phytagorean Theorem
[tex]a^{2} +b^{2} =c^{2}[/tex]
Since both all sides of a square are equal, this means that [tex]a^{2}[/tex] and [tex]b^{2}[/tex] are equal.
So that leaves us with:
[tex]a^{2} +a^{2} = 18^{2}[/tex]
Simplify
[tex]2a^{2} = 324[/tex]
Divide both sides by 2
[tex]\frac{2a^{2} }{2} =\frac{324}{2}[/tex]
Simplify
[tex]a^{2} = 162[/tex]
Find the square root of both sides
[tex]\sqrt{a^{2} } =\sqrt{162}[/tex]
a = 9[tex]\sqrt{2}[/tex]
(or if you want the decimal, rounded to the 3rd decimal place: 12.728)
