Hello from MrBillDoesMath!
Answer:
22.6
Discussion:
From the attachment, the square has sides of length "x", and the Pythagorean theorem applies. Hence
x^2 + x^2 = 8^2 =>
2 x^2 = 8^2 => divide both sides by 4
x^2 = 8^2/2 => 8^2 = 64, 8^2/2 = 32
x^2 = 32 =>
x = sqrt(32) = => as 32 = 16 * 2
x = sqrt(16) * sqrt(2) =>
x = 4 sqrt(2)
The perimeter is 4*x
= 4*(4 sqrt(2) )
= 16 * sqrt(2) => as sqrt(2) is approx 1.41
= 22.6
Thank you,
MrB