Answer:
x = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using Pythagoras' identity in the right triangle
c² = a² + b² ( c is the hypotenuse and a, b the legs )
here a = b = 6 , c = x , then
x² = 6² + 6² = 36 + 36 = 72 ( take square root of both sides )
[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{72}[/tex] , that is
x = [tex]\sqrt{72}[/tex] ← express as a product of factors with one a perfect square
x = [tex]\sqrt{36(2)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex]
