Answer:
2[tex]\sqrt{2}[/tex] x
Step-by-step explanation:
The diagonal divides the square into 2 right angles with legs s and hypotenuse x
Using Pythagoras' identity on one of the right triangles, then
s² + s² = x²
2s² = x² ( divide both sides by 2 )
s² = [tex]\frac{x^2}{2}[/tex] ( take the square root of both sides )
s = [tex]\sqrt{\frac{x^2}{2} }[/tex] = [tex]\frac{x}{\sqrt{2} }[/tex]
Thus
perimeter = 4s = 4 × [tex]\frac{x}{\sqrt{2} }[/tex] = [tex]\frac{4x}{\sqrt{2} }[/tex]
Multiply numerator/ denominator by [tex]\sqrt{2}[/tex]
perimeter = [tex]\frac{4x\sqrt{2} }{2}[/tex] = 2[tex]\sqrt{2}[/tex] x
