Answer:
8√2
Step-by-step explanation:
Idea 1 : (Pythagorean theorem)
2x² = 16²
then
2x² = 256
then
x² = 256/2 = 128
then
x = √128
then
x = √(64×2)
then
x = √64 × √2
then
x = 8√2
………………………………………………………
Idea 2 : (diagonal of a square)
16 is the diagonal of a square with side square of lengths x
Then
x√2 = 16
Then
[tex]x = \frac{16}{\sqrt{2} } =\frac{8\times2}{\sqrt{2} } =\frac{8\times\sqrt{2} \times \sqrt{2} }{\sqrt{2} } =8\sqrt{2}[/tex]