Answer:
The perimeter of the square is [tex]31.96\ m[/tex]
Step-by-step explanation:
we know that
The perimeter of a square is equal to
[tex]P=4b[/tex]
where
b is the length side of the square
Step 1
Find the length side of the square
The diagonal of the square is equal to
Applying the Pythagoras Theorem
[tex]d^{2} =b^{2}+b^{2}\\d^{2}=2b^{2}\\d=b \sqrt{2}[/tex]
In this problem we have
[tex]d=11.3\ m[/tex]
[tex]d=b\sqrt{2}[/tex] ------> solve for b
[tex]b=d/\sqrt{2}[/tex]
substitute the value of d
[tex]b=11.3/\sqrt{2}\ m[/tex]
Step 2
Find the perimeter of the square
[tex]P=4b[/tex]
Substitute the value of b
[tex]P=4(11.3/\sqrt{2})=31.96\ m[/tex]
