The right triangle formed is shown below
From the diagram,
x represents the side of the square. Recall that a square has equal sides
To find x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the diagram,
hypotenuse = 16
one leg = other leg = x
By substituting these values into the formula,
16^2 = x^2 + x^2
16^2 = 2x^2
256 = 2x^2
Dividing both sides by 2,
2x^2/2 = 256/2
x^2 = 128
Taking square root of both sides, we have
[tex]\begin{gathered} x\text{ = }\sqrt[]{128}\text{ = }\sqrt[]{2\times64}\text{ = }\sqrt[]{2}\text{ }\times\text{ }\sqrt[]{64} \\ x\text{ = 8}\sqrt[]{2} \end{gathered}[/tex]
The correct option is 8√2 in
